Mike,
The 7970's and 79x1 phones will need to do a 2 step upgrade also. There was a change in signers for our firmware images in the firmware version 8.x that prevents old loads from validating new firmware, so you have to go through an interim load to get to the latest loads.
Check out http://www.cisco.com/en/US/docs/voice_ip_comm/cuipph/firmware/8_5_3/english/release/notes/7900_853.html#wp57602
So the best bet is to upgrade your 4.1(3) firmware that is later than 8.3(3), but before 8.5(2). Then your upgrade to 7.1(3) and eventually 8.x will go smoothly.
I am not aware of any restriction on the 7940/60, but if the release notes say you must go through an interim build, then I will deffer to that direction.
I do not believe that the ATA has the same restrictions as the 79xx phones. Also, please refer to the 792x firmware release guide for similar restrictions on the wireless phones.
Thanks,
Dan Keller
Technical Marketing Engineer