I guess this is SOP for large airline ops. In bizjets, we usually don't have the same problem with stopping so we often brief that we'll stop for anything prior to V1.
I'm quite surprised to hear that your SOPS do not include the 70 or 80kt "stop for anything." In my experience it is used quite often in both airline and corporate operations, but obviously by not all.
While I agree that the corporate jets are likely to accelerate at a greater rate, they are (probably) more often used on runways of shorter length. This being the case, and especially in the wet, I would rather initiate a "stop" immediately upon first sight or sound of any warning, rather than investigate while continuing to V1. The only harm it can do at such a relatively low speed is cause a bit of extra brake wear, and time to replace the energy dissipation.