Dude you own a $400 trout stick! You can afford the $13 for a license...LOL
It doesn't really say in the Trout regs. but I would say that yes you need the trout portion. It's funny that there is a special trout/salmon portion but you are required to buy the general tag as well!
Anyway fishing a restricted License on the Holy water, or even Tippy and telling a CO that you are fishing for warmwater fish is like dressing in camo, carrying a bow and telling the CO that you are just watching the deer.