I agree with Kelmo about being the wrong type of nuts. Should be a lock washer and non-shouldered or non-cap nut like in the pic. My 79 620 has similar carb nut access issues.
What helps tremendously before removing the carb... take a mini brass wire brush from Harbor freight .79 cents and knock as much crusty/gunky stuff out of the bolt threads you can. &/or use some Goof Off on a rag to wipe them off and loosen any thread-crap build-up, then hit the studs again with the mini-brass-brush. This helps the nuts spin on/off a lot easier, and you can spin them down with your bare fingers vs. having to turn them a 12th of a turn at a time with a wrench! Once the carb is removed, put a rag in the intake holes to prevent anything falling in, and check the bolt threads for gunk build-up again when you have better view and access.
I unsuccessfully tried the balancing act of putting the nuts on the carburetor base before lowering the carb over the studs. I typically bumped the carb and dropped some, if not all nuts and washers all down the into the intake, shrouds, and motor. Sometimes they fell thru to the ground below, often times not.
My latest and fastest method is to use a straight dental pick type tool (awl shaft without a handle, really long nail, etc.) to keep from dropping washers and nuts. After putting gasket and carb on manifold, put the sharp end of the dental pick on the top of the bolt head. Slide the washer down the shaft and over the bolt. Next, slide the nut down so it is balancing on the top of the bolt shaft. Don't remove the pick yet! I spin the nut with one fat finger to start it on the bolt thread. This pic method saves dropping your washer and nut a dozen times for each stud, and saves a hell of a lot of cursing, and hunting for dropped nuts in the motor with a magnet. The yarn method is very innovative for not dropping your wrench, but I'm not coordinated enough to keep from getting wrapped up in it while using. And the one in the pic is too short for me to manipulate easily for my old hands. I dipped the handle of my wrench in red plastic-dip to make it easier to handle, easier to see, and less slippery.
I was also going to make the suggestion Nicholas did about making the wrench thickness super-thin, but he beat me to it. The custom carb wrench doesn't need to be beefy at all. Grind it down until it's bolt shaft arms are thin, more like a fork design for easier handling and bigger turns. You can also grind off the shoulders of the bolt arms pretty thin too. The bolt opening arms only needs enough shoulder meat on the bolt sides where it grabs the bolt head (or nut) to spin the nut tight enough to compress the lock washer + a little torque. Cut the wrench handle off so it is only 3- 4" long, or just under nearest obstruction distance.
A year or two ago I was trying to make a motor run in a truck. Took the carb on/off 3-4 times to diagnose it. The first time removing it before learning these tips, it cost me removing the valve cover + cleaning the valve cover + a new gasket, plus an 1 1/2 hours of my time just to get the carb off, plus a hell of a lot of frustration.
The last time I R&R'd the carb it only took me 10 minutes and I didn't remove the valve cover. It was late, cold, and dark, and I'd already had a couple beers. I just finished putting the carb and throttle cable on, connected the fuel line, had all the vac lines blocked off because I hadn't yet put the air cleaner back on. Got my head out from under the hood and stepped away from the fender. Turned to reach in the open window to start it up to test my work...noticed the carb gasket safely leaning on the windshield out of harms way. Doh! I forgot to install the carb gasket! R&R practice makes perfect. LOL