Ok, I just noticed the OP is dated. But FWIW:
When my parents died, I got some estate money and wanted to blow some of it on a cycling adventure. Wound up taking a catered tour from Lhasa to Kathmandu. When I signed up, I didnít quite realize that Lhasa was not in Nepal. The blurb just said the average elevation was 17000. Well, not quite. We had several passes that were either pushing or over 17000í (17200 max), but the average was probably 13000 +.Couple of days at Everest base camp and 16500 ft.
I had to do the trip again the next year because I couldnít handle the altitude and had to evacuate to KTM the first time. Went back with the proper meds and managed to do whole tour + another two week tour in Nepal (KTM, Hetuada via Tribhuvan road, Chitwan park, Bhutwal, Pokora , Gorkha, bus to KTM).
It was a wonderful trip. Love Nepal and Iíve returned twice more including a 5 mo homestay during the monsoon on the border of Chitwan. Chitwan is in the Terai and is basically still the Indian plain, so it was not a great place to be during the high heat before the monsoon. It was still 90+ and high humidity after the monsoon cooled things off.
This doesnít answer your question at all. I hope that it does give some credibility to my insistence that you do this race, or something similar.
My experience was with Himalayan Mountain Bike(HMB) which has also put on races with international fields. I couldnít find a current web site, but I didnít look real hard.
I did find this link to a company called ďDawn to DuskĒ. They also have a small shop in Thamel (touristy area) in KTM. Iíve down business with him and was favorably impressed. I found this link
Dawn to Dusk race - Annapurna
I recognize these names as being on the Annapurna trek, one of three standard treks. Note that the Throng La (la means pass) is over 17000 feet. I canít compare this with any other similar race, but it would really excite me and I think I know the area and the company well enough to provide a recommendation.
At the very least, whatever you want to do, just DO IT. Itís a bucket list experience.