I know that carrier exclusives work on their respected carrier, like 822, 928, icon to verizon and 1020 and 1520 on AT&T. What about other phones, like the global ready phones. Would the 929 or 1320 work on either of these carriers?
Every phone has unique antennas in it, so it is entirely model specific what carrier they work on. Do note as well, just because a phone is GSM doesn't mean it will work on EVERY GSM network and same for CDMA and LTE.
Also, the 929 (Icon) is designed for Verizon's network but should also work (3G and LTE) on AT&T's network as well. The 1320 should get 3G on both carriers but will definitely not be able to receive LTE on either.
There is a variant of the 1320 which gets LTE on TMO. You need to know the variant for each phone and also find out what bands the phone has and what bands the carrier supports. Wikipedia is a good source for both finding bands on phones and frequencies of various carriers.