Since you're not able to add your User-Defined apps over to the Hosted Applications list, what about if you tried to add the default applications to the Hosted list? My thinking is if you add, i.e. Mechwarrior 4 to the Hosted list, find what port to open for that game, and then have Minecraft bind to that port instead of 25565, the firewall will allow traffic to that "default defined" app port.
Could it be that the rules you made are wrong? That's the only explanation I can think of that would prevent the firewall from whitelisting the Minecraft ports. Granted, specifying the IP of the computer running Minecraft and the port is not hard at all but we're scraping the bottom of the idea bucket (not to mention if there was an actual problem then you shouldn't be able to save the rule).
Another thing you can try is to add another User-Defined rule for a default app that already exists. Going back to Mechwarrior 4, say it uses TCP port 35565. Can you create a rule and move it over to the Hosted Application list? Can you move anything to the Hosted list?
If this networking pos device still refuses to whitelist anything, you could try and put your computer in the DMZ. Yes, it isn't recommended to do so but if all your programs are up to date, and you only allow Java through the firewall, the danger is slightly mitigated.