CHECK THE DRAIN VALVE
Just for the record, the gasket you needed is Hobart part number 435544 and has a list price of 2.20. So the guy really overcharged you but since you were getting the support and did not have to pay the separate shipping, I guess it was a fair price.
Just know, that these gaskets do have a tendency to stretch a bit and will appear to be too big when you want to reinstall the old ones. No harm would be done if you actually cut it just a bit to fit the circumference of the lower support. Just make sure that the is no gap in it.
As far as "forcing" a drain cycle, you should hear a definite "snap" sound of the drain valve energizing during the cycle. If you advance the time knob by hand when it is in the wash cycle( a cycle button needs to be pressed (like normal or soak cycle) you will come to the portion of the cycle where the water needs to drain and hear that snap. If you don;t, then you likely need a drain valve.
If you cannot find one online, then let me know as I have a few of them and I know Combo52, John has some.
I do have a rinse dispenser for the machine too if you want to install one.
As far as the door opening too low, it would seem that the hinges have either worn out or someone stood on the door or leaned on it to heavily at some point in its live and you will need to replace them. If you can pull the machine out of the counter a bit, you can see exactly is wrong with them. the stops on the hinges should contact the side frame of the tank when the door is perpendicular to the tank. If the hinges still have more travel, they are bent. Also, you will be able to see if the flange of the tank has been bent out which may be hard to fix, though not impossible. This condition can also be cause by repeatedly letting the door drop when opening it especially if the wood panel is heavy and they did not get the heavy duty door springs.