In terms of cave diving, I don't want to do a lost line drill in some portions of Manatee either, so saying that large size is an issue wth a lost line drill in ice diving is a bit sort sighted.
The issue on an ice dive using cave techniques is to not to get too far off the line before you stop and do the drill. Worst case you screw up badly get 20-30 feet off the line and realize you are silted out. Tie off to and drop a back up light etc on the bottom and gently to a circular search pattern until you encounter the line. It's just not that hard to do, and no worse than a couple hundred zero viz searches I have done in commercial and PSD situations.
I have in the past done ice dives with a line similar to a cave dive (tie the shot line to an ice screw on the surface, do a primary tie off on the shot line, a secondary on the bottom if able, and then conduct the dive like you would any other cave dive using rocks, logs, etc for placements when available and PVC stakes when nothing is available.
Now, when doing this I will not take any diver with me who is not cave trained and who does not have superb buoyancy and fin techniques.
Freeze flows are a distinct possibility but the ability to shut down a freeflowing post and swap regs ensures a constant gas supply - and after a few mnutes you can turn the freeflowing post back on as the reg will have thawed and will no longer freeze flow.
One thing I would never consider doing however is an ice dive in current, unless the current is flowing toward open water with no possibility to switch directions.