The older boxes were all "sealed for life" type and I never had any trouble with the one in my Omega even though it was quite high mileage. Is the box causing you a problem that steers you towards a box problem?. There is a filler hole on at least the 2.0 engines and as I remember Haynes says the level should be up to the top of the hole on level ground etc etc also there is no dipstick on these you could just remove the plug with an allen type key and have a look.
You start the engine and when everything is up to operating temp and the car on level ground (not jacked up on one side or anything like that, you put it into the fill hole on the side (driver's side IRRC) until it runs out, and then run the shifter through the positions and top up again. The correct fluid is Texaco 7045E which is the lifetime fill. You should be able to topup with Dexron IIIG.