That is a difficult trade-off. $350 per month is significant, but a migration can also become a substantial hit once you account for the engineering time, operational changes and risk involved.
I dealt with a similar situation before, and one thing that helped was establishing exactly what would need to move before estimating the migration.
With PHI, that scope can be wider than it first appears. It is not only about where the database or backend runs. PHI can also surface through requests, logs, analytics, caches, previews and error reporting.
Mapping those paths gave us a much clearer picture of the real migration scope and changed how we evaluated the decision. It may be worth doing that before committing either way.