I realize there are arguments both for and against umbilicals. I'm not getting into that. Presupposing you have decided to use an umbilical for whatever reason, wouldn't it make more sense to have it clipped into your lead rope, rather than directly to your belay loop, with some kind of screamer like connection between the umbilical and the belay loop.
In this manner, your top ice tools is always your highest piece of pro, and your tool is loaded dynamically with the stretch of the rope in the system absorbing energy, rather than statically onto a short tether.
Obviously this only matters in the rare case where you've severely screwed up and are taking an ice fall...which you shouldn't do...so I get that this isn't a very big use case, and may not be worth the additional complexity.
I've illustrated what I mean here: https://docs.google.com/presentation/d/1fZdgCsvWbuJ2uX5KyzKSg1wnJ0YZunvsX8BjsDfvLho/edit?usp=sharing