Just brought 6 bags (relocating cross-country this week) on a UA flight. Charge was $185 for the extra bags (took one carry on).

Just pay the extra $$ - that way you'll make sure you get the bags there. The cost is minimal re: the hassle of not getting them there. One other note: if the supplies, etc. are important (as it sounds like they are), then I would make sure that all of the medical supplies are in my carryon that I take with me on the flight.