Just called them back and asked to be transferred to IT/web support and they said they don't do that, FWIW. Hoping this rep can help. She's at least asking questions no one else has asked so far.

ETA: I got transferred to a rep who I thought was going to be able to help, and then our connection dropped. :/ He did tell me that the only way to transfer miles is via the online form, but he was willing to try to help me figure out why it wasn't working. After much troubleshooting, we can not figure it out. I sent him a screenshot and he noticed that the Save button on the form is in a different location for me than it is for him - for me, it appears in the upper right corner of the form, for him it's in the lower left. He pretended to transfer miles to me and it worked just fine. He was using the same version of the same browser that I am. We have tried 4 computers, 2 phones, 3 browsers, wifi, mobile data, and a VPN.

Is there something about one of our SkyMiles accounts that could be causing the form to reset WITHOUT giving an error message? We are not getting any errors... the form simply refreshes and all data input disappears. It seems highly unlikely that it's a hardware error on this many different devices and browser combinations, so I'm now questioning what else could cause it.

If anyone is willing to log in and pretend to fill out a transfer miles form, please let me know what browser and device you use and where the save button is for you. Any advice is welcome. Thanks.