I wasn't up for conlanging today, so I'm going to quickly mention some ideas I had shortly after the last post, for trying to deal with the issue.
Somewhat weird option: put the meaning verb in the genitive, since the genitive doesn't exist on its own in normal sentence structure.
Somewhat bulky option: put it in the accusative, but require some form of determiner for all noun phrases. The latter part sounded to me like an interesting touch, regardless of whether I go with that actual solution. It would basically be like "some of the other languages I know, but more". "My thing"? No, "The my thing". (All right, "The thing of mine".)
In any case, if the verb isn't taking a determiner because it's not a noun phrase, then that means I could put it in any case I want. I choose... nominative. That way, when a verb is participating in this system, it's always nominative, regardless of the aspect.
That is my initial feeling on this idea.
Anyway, that's way more than I expected to get accomplished here today, good job me, I need to get ready for bed now, wow, so tired.