A833 OD or 727 behind a 440. Suggestions and questions

I wish I knew for sure what gears I have in mine.

Guess I will have to eat the cost of a gasket and check.
Actually you have two other options.
The first is to just turn the axles and see how many times the driveshaft turns, and some simple math spits out the ratio.This is dead-nuts accurate.
If you have a SG you just get both wheels up, mark the tire and D/S and turn the tire one exact complete revolution, counting the D/S revolutions as you go. A 3.55 gear would totate the D/S about 3.5 revolutions; a 4.10 would turn a tic over 4 revolutions; etc.
With an open diff, you only jack up one side, and now turn the tire Two full revolutions.

And the second is to do the math at speed versus rpm. This is not very accurate with an automatic, but will usually get you within 10%, sometimes 5%, if your speedO is accurate .