Both Sprint and T-Mobile were less than truthful. They were either ignorant of the facts, or they simply lied.
The phone will work on T-Mobile if unlocked. There is no financial incentive for Sprint to unlock your phone. When they do so, you will leave their network. There is also no financial incentive for T-Mobile to help you bring your Sprint phone to their network. They will make more money if you buy a new phone.
Get hold of Sprint again and escalate the call. Threaten to involve the FCC and the FTC if you have to.