I run 35s on stock 3.54 gears and I don't air down. I've also driven around in 2wd on the sand and been just fine. You should be fine regardless of your engine size or gearing. I would wonder if something is wrong with your carb and/or ignition to cause it to bog down and stall.
I will say the sand has been really loose the last week or so due to lack of rain.
Here's something to help you eliminate driveline as a problem. Get the jeep on a steep slope...dirt or loose gravel or even wet grass...something you won't be able to climb. Put it in 4wd and try to climb the hill while applying slight brake pressure. The braking will overcome the 2 wheel spin of the open diffs and you should be able to get all 4 wheels to spin simultaneously. Once all wheels are spinning at once, you know you have no binding/axle issues. Just be aware that too steep an angle might cause a stall because of the float bowls in the carb.