Hard to go wrong with either Global Rescue or Ripcord.
We have used both in my business (currently use GR)... No complaints on either side..
Ive currently got guys in a handful of central African countries, a couple of east African countries, a couple of central American countries, etc.. wonderful garden spots like Somalia, South Sudan, etc.. and never had so much as even a minor problem.. to include having to do a couple of medical evacuations while South Sudan was in the middle of a civil war (non combat related medevac)..
FWIW, there are a number of decent hospitals/medical facilities in Uganda if you are in need of immediate relief for something.. Nowhere I'd want to go for cancer treatments, etc.. but for a more typical "out in the wild" type injury or malady (laceration, broken bone, etc or picking up a case of food poisoning, malaria, etc..).. Treatment would be absolutely ok..
When I had a team of US and European expats working for us in Uganda, they used the Kampala Independent Hospital and the International Hospital in Kampala.. There was also a clinic in Entebbe that they used a bit I believe, but I cant remember the name..
FWIW I got a BAD case of food poisoning in Juba in 2016 that had me laid up in an international clinic for a couple of days.. my doc was a Ugandan national that had been trained in France.. He actually took very good care of me.. between him and the retired USAF PJ we had assigned as our camp medic, I was back on my feet and feeling ok within a few days, despite painting an entire room with about 15lbs of projectile vomit and poo just 72 hours prior... Its been a few years since I last checked.. but Im pretty sure he is working at KIH now (one of our expats in Uganda had transferred there from Juba and told me that a couple of years back)...