Simply put, this is not going to happen. The old forum system was heavily modified to be able to interact with TQ and Eve Gate. Unfortunately, we have gotten to a point where both Eve Gate and the old forums are/were on the verge of collapse. For example, just try and load Eve Gate and you will notice that it may take 10-15 seconds for some of those pages to load.
The big issue here is that with Eve Gate being unstable, tying the forums in to Eve Gate would make the forums unstable. By keeping the forums as separate from Eve and Eve Gate as possible, these forums stay online even when Eve is offline. So long as you log in here before SSO falls over, you can still post on these forums. Even if you don’t you should still be able to browse these forums.
In-terms of Eve Gate, I am not sure how it ties into Eve, but given how long it’s performance has been terrible, I am going to assume they did some wizardry there to make it work in the first place. With the use of ESI, most of the functionality of Eve Gate is now obsolete anyway.
CCP may make changes in the future to further integrate the forums with Eve but they may not as well. For now, your best bet would be to access Eve Gate here: https://gate.eveonline.com . Or use any number of third party websites, or cell phone applications if you want to be able to manage your eve mails while you’re not in game.