Thanks very much for your help. I wanted to follow up with the resolution in case anyone else was having the same issue. I used the following commands as instructed in the link provided by Pilgrimsmaster:
hf 14a config --atqa force --bcc ignore --cl2 skip --rats skip
hf mf wrbl --blk 0 -k FFFFFFFFFFFF -d 11223344440804006263646566676869 --force
hf mf wipe --gen2
What was interesting is that it actually took a few tries in order to get it to work successfully and I have absolutely no idea why that is because I didn’t change anything between the attempts apart from start over from the beginning after getting a string of errors when I tried to run to wipe command the first time. At any rate, it worked just fine the second time so I went back to attempting to clone my 9691T using:
hf mf restore
This worked without issue, but the ring would not open my lock. I dumped to text the contents of both the ring as well as the original fob and then used diff to compare the output. They were identical except for the latter half of block 0 on the ring. The UID on the ring was showing the same as the fob, but the rest of the data in that block was still what I had written to block 0 in the command above. Thus, I just ended up using the command:
hf mf wrbl --blk 0 -k FFFFFFFFFFFF XXX —force
where XXX was the value in block 0 on the fob in order then write it to the ring. The ring works perfectly now.
Cheers!