The reason why the first sentence "What I feel more important is for you to go home right now" appears ungrammatical is quite complex and has to do with the expletive (or dummy) it and cleft sentences.
The expletive it has the function of anticipating what follows:
I find it useful to take notes while reading.
I believe it necessary that I know who I'm talking to.
I think it important for you to go now.
If you wish to emphasise what you find useful, important, etc., you can make a cleft sentence as follows:
What I find useful is to take notes while reading.
What I believe necessary is that I know who I'm talking to.
What I think important is for you to go now.
On this basis, the OP's cleft sentence is derived from the sentence:
I feel it more important for you to go home right now.
But for me, the expletive it does not sound right with feel, and hence the cleft sentence based on it also does not sound right. The more usual starting point would be:
I feel (that) it is more important for you to go home right now
resulting in the cleft sentence (and second OP example):
What I feel is more important is for you to go home right now.