Thanks for the new design - #34. The 6-armed cross is indeed a pretty universal medical symbol; unfortunately it's recognized as such much less in the U.S. than elsewhere, so it really won't work.
I took a look through your portfolio (wow, lots of fantastic logos!) and found a few I really like:
The PUre Spin logo is really nice. SOmething like that in red and blue, with the text around the perimeter, and an image in the middle of a very stylized cross, or a stylized image of a doctor..???
EnvironMetal Recycling looks super-cool to me: maybe for the graphic symbol use the caduceus (very universally-recognized symbol of healthcare)
C To C Tile is a really classy and edgy look. Maybe take something like that with either the classic 4-armed cross as the symbol to the left, or some version of the caduceus, and the text in a lighter color against a red or blue background.
Those are just some ideas I get from some of your other designs I really like. Hopefully these comments give you some ideas...I really appreciate your hard work on this, thanks!