To be clear, are you going to be self-hosting Tealium? If so, and our utag.js is hosted on the same domain as your site, then you could in theory create a post request, but I would not recommend it.
When you say "large custom tags" are you talking about the JavaScript files themselves? The 2083 character limit only applies to the actual URL of a file, and has nothing whatsoever to do with the file itself. Furthermore, this knowledge base article suggests that the limit applies to both POST and GET requests, so using POST requests to circumvent the issue probably wouldn't work:
http://support.microsoft.com/kb/208427
There are rarely going to be occasions when you hit the character limit, and in the case of Adobe SiteCatalyst which uses the query string very heavily, there is a built-in variable compression algorithm to avoid this problem.
Hope this helps!
Craig.
Check out our new Swift integration library for iOS, macOS, tvOS and watchOS: https://github.com/Tealium/tealium-swift with updated
documentation https://community.tealiumiq.com/t5/Swift/tkb-p/swift.