If you have a problem with medical, but still feel confident you can complete the proposed flight safely.... there is another option besides sport pilot: Glider pilot. No medical required (you can have even failed your medical, and, unlike sport pilot, you don't have to regain your medical (a sport pilot has to, before transitioning to the sport pilot "driver's license medical")
Empty weight of a Pipistrel Sinus motorglider is 628 pounds. Since the max takeoff weight is 1323 pounds ...that leaves 695 pounds of gas and passengers. Normal fuel tank is 16 US gallons (104 pounds of fuel) but mine has the "long range" 25 gallon fuel tanks (2 x 12.5 wing tanks, for 169 pounds of fuel) leaving me 526 pounds for people, flight gear, baggage, and in-flight refreshments. It seats 2 people. It has a max speed of 120 knots (VNE is 122) while burning less than 4 gph; cruise is 110 knot , and gives a range of some 650 nm.
Unlike a light sport pilot, a glider pilot can legally fly at night (with properly equipped aircraft) and above 10,000 feet.
Also, many of the Sinus aircraft in the US are registered as Experimental aircraft and thus could be equiped for IFR flight and flown in IMC (though it does not have protection against lightning, and so shouldn't be flown near where this may occur). My Sinus, howerver is a SLSA glider. Not experimental.
It also has a fully feathering prop, to provide a glide ratio of up to 27:1, just in case you actually do want to try your hand at soaring.
Oh, and Pipistrel? It has an impressive engineering department, allowing their aircraft to win a couple of NASA flight competitions. And it is now a subsidiary company of Textron, and is a sister company to Cessna and Beechcraft ...