2007 yz450f hot start cable

I am a proud owner of a yz450f that won’t run. I purchased this bike a couple weeks ago. It was running when I picked it up. I was told the hot start cable needed replaced as it was broke.
I went to replace it and found someone had used some type of glue to keep the fitting in the carburetor and the cable was not attached to anything.
I’m trying to get it out and have parts on order.
I have now run into a problem where the bike is hard to start and shuts off quickly after running for a moment.
My question is, should I replace the carburetor vs rebuilding, since I have no clue the conditions of the threads for the fitting or if I can clean it out. And if I replace it, any suggestions on manufacturer of the carb as Yamaha wants $1300 for one.

any other suggestions would be much appreciated!