diff --git a/Casks/e/eloston-chromium.rb b/Casks/e/eloston-chromium.rb
index cf451d2e7a..203e2dd72d 100644
--- a/Casks/e/eloston-chromium.rb
+++ b/Casks/e/eloston-chromium.rb
@@ -16,12 +16,19 @@ cask "eloston-chromium" do
   desc "Google Chromium, sans integration with Google"
   homepage "https://ungoogled-software.github.io/ungoogled-chromium-binaries/"
 
+  # Releases are separated by architecture, so we have to check multiple recent
+  # releases instead of only the "latest" release.
   livecheck do
-    url "https://github.com/ungoogled-software/ungoogled-chromium-macos/releases?q=prerelease%3Afalse"
-    regex(%r{href=["']?[^"' >]*?/tree/v?(\d+(?:[.-]\d+)+)(?:[._-]#{arch})?(?:[._-]+?(\d+(?:\.\d+)*))?["' >]}i)
-    strategy :page_match do |page, regex|
-      page.scan(regex).map do |match|
-        (match.length > 1) ? "#{match[0]},#{match[1]}" : match[0]
+    url :url
+    regex(/^v?(\d+(?:[.-]\d+)+)(?:[._-]#{arch})?(?:[._-]+?(\d+(?:\.\d+)*))?$/i)
+    strategy :github_releases do |json, regex|
+      json.map do |release|
+        next if release["draft"] || release["prerelease"]
+
+        match = release["tag_name"]&.match(regex)
+        next if match.blank?
+
+        (match.length >= 2) ? "#{match[1]},#{match[2]}" : match[1]
       end
     end
   end
diff --git a/Casks/e/extraterm.rb b/Casks/e/extraterm.rb
index 7b073d1d1a..eb6a9ddbfc 100644
--- a/Casks/e/extraterm.rb
+++ b/Casks/e/extraterm.rb
@@ -12,9 +12,20 @@ cask "extraterm" do
   # This should be updated to use the `GithubLatest` strategy if/when stable
   # versions become available.
   livecheck do
-    url "https://github.com/sedwards2009/extraterm/releases"
-    regex(%r{href=["']?[^"' >]*?/tag/v?(\d+(?:\.\d+)+)["' >]}i)
-    strategy :page_match
+    url :url
+    regex(/^v?(\d+(?:\.\d+)+)$/i)
+    strategy :github_releases do |json, regex|
+      json.map do |release|
+        # This omits the usual `release["prerelease"]` early return condition,
+        # as we need to work with pre-release versions for now.
+        next if release["draft"]
+
+        match = release["tag_name"]&.match(regex)
+        next if match.blank?
+
+        match[1]
+      end
+    end
   end
 
   app "ExtratermQt.app"
diff --git a/Casks/f/forkgram-telegram.rb b/Casks/f/forkgram-telegram.rb
index ccca856bdc..9592d9a9e2 100644
--- a/Casks/f/forkgram-telegram.rb
+++ b/Casks/f/forkgram-telegram.rb
@@ -10,28 +10,22 @@ cask "forkgram-telegram" do
   desc "Fork of Telegram Desktop"
   homepage "https://github.com/Forkgram/"
 
-  # NOTE: This approach involves multiple requests and should be avoided
-  # whenever possible. If upstream starts reliably providing the macOS zip
-  # files in every release, we should switch to `url :url` with
-  # `strategy :github_latest`.
+  # Not every GitHub release provides a file for macOS, so we check multiple
+  # recent releases instead of only the "latest" release.
   livecheck do
-    url "https://github.com/Forkgram/tdesktop/releases?q=prerelease%3Afalse"
-    regex(%r{/v?(\d+(?:\.\d+)+)/Forkgram[._-]macOS[._-][^"' >]*?#{arch}\.zip}i)
-    strategy :page_match do |page, regex|
-      # Collect the release tags on the page
-      tags = page.scan(%r{href=["']?[^"' >]*?/releases/tag/([^"' >]*?)["' >]}i)&.flatten&.uniq
+    url :url
+    regex(/^v?(\d+(?:\.\d+)+)$/i)
+    strategy :github_releases do |json, regex|
+      file_regex = /^Forkgram[._-]macOS[._-].*?#{arch}\.zip$/i
 
-      max_reqs = 4
-      tags.each_with_index do |tag, i|
-        break if i >= max_reqs
+      json.map do |release|
+        next if release["draft"] || release["prerelease"]
+        next unless release["assets"]&.any? { |asset| asset["name"]&.match?(file_regex) }
 
-        # Fetch the assets list HTML for the tag and match within it
-        assets_page = Homebrew::Livecheck::Strategy.page_content(
-          @url.sub(%r{/releases/?.+}, "/releases/expanded_assets/#{tag}"),
-        )
-        matches = assets_page[:content]&.scan(regex)&.map { |match| match[0] }
+        match = release["tag_name"].match(regex)
+        next if match.blank?
 
-        break matches if matches.present?
+        match[1]
       end
     end
   end
diff --git a/Casks/f/free-gpgmail.rb b/Casks/f/free-gpgmail.rb
index 4ec02a5d27..a50b1a8548 100644
--- a/Casks/f/free-gpgmail.rb
+++ b/Casks/f/free-gpgmail.rb
@@ -25,16 +25,23 @@ cask "free-gpgmail" do
   # cask `version` (based on the execution environment). As such, this won't
   # surface a new major version and that will need to be handled manually.
   livecheck do
-    url "https://github.com/Free-GPGMail/Free-GPGMail/releases?q=prerelease%3Afalse"
-    regex(/.*?Free-GPGMail[._-]v?(\d+(?:\.\d+)*)[_-](\d+(?:\.\d+)+)([_-][^"' >]+?)?[._-]mailbundle\.zip/i)
-    strategy :page_match do |page, regex|
+    url :url
+    regex(/^Free-GPGMail[._-]v?(\d+(?:\.\d+)*)[_-](\d+(?:\.\d+)+)([_-].+?)?[._-]mailbundle\.zip$/i)
+    strategy :github_releases do |json, regex|
       version_suffix = version.csv.third&.sub(/^[_-]/, "")
-      page.scan(regex).map do |match|
-        next if match[0].split(".").first != version.csv.first.split(".").first
-        next if match[2]&.sub(/^[_-]/, "") != version_suffix
 
-        "#{match[0]},#{match[1]},#{match[2]}"
-      end
+      json.map do |release|
+        next if release["draft"] || release["prerelease"]
+
+        release["assets"]&.map do |asset|
+          match = asset["name"]&.match(regex)
+          next if match.blank?
+          next if match[1].split(".").first != version.csv.first.split(".").first
+          next if match[3]&.sub(/^[_-]/, "") != version_suffix
+
+          "#{match[1]},#{match[2]},#{match[3]}"
+        end
+      end.flatten
     end
   end
 
diff --git a/Casks/o/obs-websocket.rb b/Casks/o/obs-websocket.rb
index 4e2b17e403..3b6b46b568 100644
--- a/Casks/o/obs-websocket.rb
+++ b/Casks/o/obs-websocket.rb
@@ -11,9 +11,8 @@ cask "obs-websocket" do
   # "latest" release may be for an older major version. Unless/until this is
   # resolved, we have to check more than just the "latest" release.
   livecheck do
-    url "https://github.com/obsproject/obs-websocket/releases?q=prerelease%3Afalse"
-    regex(%r{href=["']?[^"' >]*?/tag/v?(\d+(?:\.\d+)+)[^"' >]*?["' >]}i)
-    strategy :page_match
+    url :url
+    strategy :github_releases
   end
 
   pkg "obs-websocket-#{version}-macOS.pkg"
diff --git a/Casks/w/wine-stable.rb b/Casks/w/wine-stable.rb
index 74dc604512..4559fc5cf8 100644
--- a/Casks/w/wine-stable.rb
+++ b/Casks/w/wine-stable.rb
@@ -11,28 +11,22 @@ cask "wine-stable" do
   desc "Compatibility layer to run Windows applications"
   homepage "https://wiki.winehq.org/MacOS"
 
-  # NOTE: This approach involves multiple requests and should be avoided
-  # whenever possible. If upstream starts reliably providing `wine-stable` zip
-  # files in every release, we should switch to `url :url` with
-  # `strategy :github_latest`.
+  # Not every GitHub release provides a `wine-stable` file, so we check multiple
+  # recent releases instead of only the "latest" release.
   livecheck do
-    url "https://github.com/Gcenx/macOS_Wine_builds/releases?q=prerelease%3Afalse"
-    regex(%r{/v?(\d+(?:\.\d+)+)/wine-stable[._-][^"' >]*?\.t}i)
-    strategy :page_match do |page, regex|
-      # Collect the release tags on the page
-      tags = page.scan(%r{href=["']?[^"' >]*?/releases/tag/([^"' >]*?)["' >]}i)&.flatten&.uniq
+    url :url
+    regex(/^v?(\d+(?:[.-]\d+)+)$/i)
+    strategy :github_releases do |json, regex|
+      file_regex = /^wine-stable[._-].*?$/i
 
-      max_reqs = 6
-      tags.each_with_index do |tag, i|
-        break if i >= max_reqs
+      json.map do |release|
+        next if release["draft"] || release["prerelease"]
+        next unless release["assets"]&.any? { |asset| asset["name"]&.match?(file_regex) }
 
-        # Fetch the assets list HTML for the tag and match within it
-        assets_page = Homebrew::Livecheck::Strategy.page_content(
-          @url.sub(%r{/releases/?.+}, "/releases/expanded_assets/#{tag}"),
-        )
-        matches = assets_page[:content]&.scan(regex)&.map { |match| match[0] }
+        match = release["tag_name"].match(regex)
+        next if match.blank?
 
-        break matches if matches.present?
+        match[1]
       end
     end
   end