Dont worry to much about there not being a listing for the 77, aside from a minor jet change and the clips slots on the needle, the 77/78 are virtually the same.
If you can only get it to run at 4k on choke, it is most certainly assured that the whole idle circuit is dirty.
Download the 78k/f manual and look at the carb section. It will show you how to pull things apart, all except the idle jets. Those need to come out too and they can. Just wrap a cloth around the jet and grip with pliers and twist while pulling.
Now of course you want carb spray but also a couple thin strands of copper wire and soft bristle pipe cleaners. The copper is used to clean all the small holes in the jets as carb cleaner just wont cut it in almost all cases by itself.
First, you will hose down things with the spray, then depending on the part, either clean with the copper or the pipe cleaner. Spray again and clean again. Clean every where! Can't stress that one enough. Every nook should be touched no matter what it is for. Pull out every piece, everything you can and go to town. What I tell people is clean it till you would eat or drink off of it.
From there, put it all back together and then set everything to base adjustments. Middle spot for needle clip, 1.5 turns out for the idle mix screw. Remember, OUT is RICHER and IN is LEANER.
Check the whole diaphragm for the accel pump. Any tears and you need a new one. Set the gap between the pump rod and the actuator to .008.
The ride IS the adventure. The destination is just to get gas!