I would suggest that you ignore the choke issue and get it running warmed up and run it hard under load for a few mins and then kill it. Pull the plug and check it for colour. (called a plug chop)
If its a nice colour (white is lean, black is rich, aim for a grey-brown) you have the jetting right.
Get your tools out, remove that choke pot etc and throw it in the bin. Block up the vacuum line prefferably at the source.
Then using some smarts, which after reading this thread, im sure youve got, fasion yourself up a bit of a ye olde style choke lever.
Take care and think idiot when you make up whatever, that lever on the carb looks like its fantastic plastic, last thing you want is to do a fantastic job and have it work well for 10 years then have a gung ho mate get all heavy handed and break the thing.
Not sure how it all fits under the cover. But im sure with a rod, some extra straightened out wire the same guage, you could make something up, run it through some bits of tin plate with holes in it as a guide. With a spring you could have it work opposite, it sits off, and you hold your finger on it to close the choke, motor starts then you let the choke off. Have it in a spot where its not proud of the outer housing. Not sure it you could get it anywhere near the control pannel.
Im assuming it gets itself up and revving Ok and only needs the choke for the initial start.
Interesting reading about the problems.
I have a chinese generator here but its a bigger one with a gravity fed tank. Missing the remote. Was missing the key too but i made one. Im wondering if i should get a remote, not so sure it would have much benifit.