We ran into the same issue with the “score builder” in HubSpot not playing nicely with external health scores.
Our setup is pretty similar to yours: we calculate a dynamic score outside HubSpot and sync it back to a custom property.
Here’s what we ended up doing (in case it sparks any ideas):
- We skipped using HubSpot’s built-in health score feature altogether. Instead, we use our own “Health Score” property (calculated externally) and built custom reports and views around that. Our CS team can sort and filter accounts by score, trigger workflows, and build alerts off it.
- We paired it with “Health Status” as a separate property. This is a dropdown field like “Healthy / Neutral / At Risk” that we can update via workflow rules or manually. It gives us something easy to filter and act on, even when the numeric score itself is super granular.
- For visibility and action, we:
- Created custom views for the CS team sorted by score and upcoming renewals
- Built Slack alerts and task reminders off specific thresholds
- And used it to trigger playbooks or email nudges when things dip
So the combo of syncing your score to a property + using companion fields and workflows can still give your team what they need.
Here’s the full write-up of what we did if you want more detail: Build a customer health score in HubSpot
Hope that helps or at least gives you a jumping off point! 
Allan @ Arrows