It looks like from a hardware perspective the T-Mo V20 is partly LTE compatible with AT&T and fully compatible on non-LTE bands, so you should be good to go hardware-wise (just maybe not on LTE).
Most of AT&T's LTE deployment is done in the 700MHz spectrum (bands 12, 14, 17, 29). They only use bands 2, 4, 5, and 30 as "additional" bands where they need extra capacity. Of those bands, the T-Mo V20 supports 2, 4, and 5. So LTE compatibility will be rare. Possible, especially in more congested areas where AT&T has been forced to add another band, but I wouldn't count on it.
Having said that, AT&T uses 850MHz (band 5) and 1900MHz (band 2) for 3G (up to HSPA+). The T-Mo V20 supports both of those bands. So you should at least be getting a 3G (GSM, EDGE, HSPA, HSPA+) signal on AT&T with your T-Mobile phone.
So APN and then swapping the SIM seem to be the next two logical steps.
The overlap between AT&T and T-Mobile bands is nowhere near 100%, sadly, especially in rural areas where neither carrier has been forced to deploy "expansion" frequencies to offer up more choices for signal. Here in Maine, of the 5 unlocked AT&T phones I own and tried on T-Mobile, only two (my Moto X 2014, and Samsung Note 4) has ONE LTE band in common with T-Mobile that happens to be used around here (Band 4) and UTMS compatibility is nonexistent with anything I've tried, even after enabling everything in the diagnostic service menus. Fortunately for you, using a T-Mo phone on AT&T is not quite as grim.