5 hp Briggs Starting Problems

Hi All – I have a 5 HP Briggs and it is giving me fits.
Model 130202
Type 3116-01
Code 88051627
I choke the carb, pull a few times and she will pop. Pull the throttle back to half way, pull about 6 times and she will run and die after about 30 seconds. Repeat the process and it is even tougher to get her running. Have to put the rope about three times as many to get her started a second time, if at all.
I pulled the carb and cleaned it, Jet, pick up tube, and body of carb. Pick up tube has no crack in it. Also, cleaned fuel tank. Installed a new diaphragm. Put it all back together and the same thing.
I sprayed a good amount of carb cleaner down the hole the other day and pulled the rope a few times with the plug out. Put the plug back in and she fired right up. Split some wood but she stalled real easy. I had to feather the hydraulics to split wood to prevent it from stalling, even though it did about a half dozen times.
Went out today to try and start it again and I am back to square one. I have not tried spraying any carb cleaner down the plug hole this time.
I have about 35 psi of compression if my gauge is correct. Gauge is about 25 years old but is in good shape.
Can anybody help???

I would be looking at the valves......needs to be up over 60psi

Compression gauges are not usefull on these small engines.

On this model engine, the tank has a reserve cup under the carb, that gets rusty over the years, and develops holes in it, and gas needs to not leak out of this cup, or you will have a lot of trouble.
With the carb back off, inspect the cup again, and go ahead and fill it and see if it holds gas. I have sanded out these cups, and put in a layer of jb weld, and has worked.

Here is a tank off of a different model, but it has a similar cup.