TPMS for steel FJ Cruiser wheels on 2013-2014 Tacoma Sport

I've done lots of reading and can't get a recent or definitive answer on TPMS for this particular conversion. I also see some evidence of a TPMS change after 2012.

My 2014 DCLB Sport came with 17" alloys. The FJ Cruiser steelies were manufactured in 12/12 and came from Wheels Express Online without sensors (I wasn't expecting them of course).

I've read there is a 20o vs. 40o difference in the sensor angle that prevents the sensors from being interchangeable from steel to alloy.

So here are the questions:

1. Can alloy TPMS sensors work in the steel wheels?

2. If not, can I look for an FJ Cruiser TPMS sensor specific to steel wheels, or might a sensor from a Tacoma steelie work better?

3. Where might I get OE or aftermarket part numbers to help less-than-fully knowledgeable sales staff?

4. What is the easiest way to get the reprogramming done? I like to give as much business to my local tire guy and stay away from the Toyota Dealer.

Thanks!

 

I suppose another option is to find a programmable sensor to which I can assign the same codes and avoid reprogramming my truck and paying the dealer $160.

This Schrader programmable appears to serve as the prescribed replacement for nearly every Toyota OE part number. They're about $48 each through Amazon, and you can buy the programmer for $250. But Why TPMS
lists a few shops nearby that would likely be able to do it as part of the on-the-rim-and-out-the-door price.

I figure if I buy through Amazon Prime it's easy and free to return if it's not correct.

 

I feel like it's be easy to trade sensors with someone who has steel sr5 wheels and is looking to upgrade to alloys (like me if I found a set close by).