I see a number of problems here:
K doesn't understand poly and you are pushing for a poly relationship
K & T are FORMER friends. K will see this as a competition (T might also). Basically you have instigated a pissing match where no one can win.
You may have to approach this from the mono standpoint (since K doesn't get poly). T is your friend. If you plan to keep your relationship with K, it can't move beyond that until he can accept being in a poly relationship.
You have a lot of stuff going on - take a step back and slow down. Not everything will be solved at once. Take one step at a time and expect to slip down a few and have to climb back up the same steps again.