So it's not a simple question at all.
I didn't mean to imply that it's simple, which I hope I captured in my second hunch and spherical cow reference.
If I had to place money on the biggest impact, it would be on the increased ice mobility directly leading to or making possible displacement of floes, particularly longitudinally. That could change overall energy balances, albedo and melt rates, disrupt freshwater lensing, possibly impact circulation patterns and other energy transfer mechanisms, and more.
But, I can't picture any effect of impact or collision, as opposed to export, that would be both persistent and significant enough to matter in the face of many orders of magnitude of difference in energy involved.
My point in emphasizing the numbers is that I would focus on the ice export, and that's already something we watch assiduously. The very same ratio demonstrates that it takes much less energy to export ice than it does to melt it in place.
So, my wager would be that intra-basin effects aren't likely to be large enough to count in the grand scheme, but I would watch all ice velocities with greater attention.