Read through all the support you have received here and it's all good advise!!!
A couple of things that haven't been mentioned though. You should flush out the gear case. The milkshake looking oil, will still be in there covering the inside of the case walls and the gearing. I would suggest filling the case with either automatic trans fluid, kerosene or even diesel fuel. Then with the case in neutral, spin the prop shaft with some form of rotating tool. Drill, impact driver whatever you have that you can attach a socket to it and the prop shaft nut. I'm not talking about spinning the shaft at 10 thousand RPM; but just fast enough to splash that solvent around. Afterwards drain the case, if it still looks milky repeat again until it looks clear. The three fluids I mentioned are are oil and will not hurt anything; just allow it to drain completely and then add the new gear oil.
As for pressure testing the gear case, you can make up your own tester; I've made a few when I was playing with outboard motor repairs. Find yourself a cheep automotive cooling system pressure tester.
Remove the rad attachment end of the tester's hose. Now find hollow fittings that will thread into the case's fill hole and that will fit the male threads of the tester's hose. Sometimes to coble this up can be difficult to find all the fittings. In that case, I'd find a longer bolt or screw for the fill hole. Cut the head off and then drill a small hold through the bolt/screw. Now thread the screw into the motor's case, leaving enough sticking out that you can hose clamp the tester's hose to the screw. Once ready do not pump anymore then about 8 or 10 pounds of pressure into the case. Have a spray bottle of soapy water ready and go nuts looking for where the leak MIGHT be?
Sorry for the long post but how else could I have explained my thoughts? Thoughts of an old retired mechanic that sometimes comes out making perfect sense to me; but gibberish to others. LOL
Dan...