I would do Doxy first. Like you said, the Doxy will hit Ehrlichia and anaplasma better than Mino. It's one of the reasons Doxy is front line defense for early Lyme infections.
If you have Babesia, neither Doxy nor Mino isn't going to do much by them selves. You'd likely need some atovaquone, coartem, larium, or clindamycin plus quinine.
I would do Doxy, and add in artemisinin, sida acuta, and/or cryptolepis for babesia in the mean time.
Post Edited (Mustard Seed) : 6/10/2016 4:29:51 PM (GMT-6)