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Interesting. After posting this I also noticed that there's lots of sim cutters on Amazon, though they all cost more than $5. Odds are good it'll work out at the Microsoft Store.
It is possible, but it requires a workaround. The first step is to get your phone unlocked. That's easy enough. To be eligible for an unlock, you'll need to pay it off if it's on an equipment installment plan or buy out your lease if you're using Jump on Demand. After that, you'll need to have had 40 days of service on the phone. That includes service before paying off your EIP or buying out the lease. Once those are satisfied, contact T-Mobile customer service and request an unlock.
Once the phone is unlocked, you'll need to get your hands on another Verizon LTE phone(the "donor phone" as I call it). It's best if the donor phone takes a nano SIM card, and phones that take other SIM card sizes are also OK. The phone does not have to be an iPhone, and it cannot be a 3G-only phone(even if it has a SIM slot, like the iPhone 4S). You can borrow the donor phone, buy it and resell it, whatever. When you're signing up for your Verizon service, activate the donor phone. Once it works properly, remove the SIM card from the donor phone and insert it into your unlocked iPhone. Once you confirm that the iPhone works, you no longer have to have the donor phone.
If the donor phone accepts a SIM card that's larger than your iPhone's nano SIM card, you'll need to trim the SIM card down to size. I suggest using a SIM cutter.
Edit: This might not be necessary. There are reports that Verizon has started to approve iPhone 6 series phones that weren't sold by them, meaning that they can be activated officially. Before you use this guide, try to activate your unlocked iPhone like normal on Verizon. It might work.