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.
If the runway is wet or contaminated, yes the brief includes contingencies. We don't use runways shorter than 5,000 feet if they're wet. Unfortunately some corporate ops are not as standardized as airline ops...much to their detriment. The problem is that some ops don't use common sense. When I was instructing on the Falcon 2000, I gave a crew a significant electrical problem (the PF lost his panel) at 90 knots on an 11,000 foot runway. V1 was about 120-123. It was at night and 600 RVR. They took the damned airplane flying when the BFL was 3200 feet!!
You're so correct, it's about THINKING and once in a while, folks don't.