A non SA option
If you are in PVG, then KA/CX offers frequent services to HKG. From HKG, KA flies 5 times per week to KTM, landing late in th evening in KTM. Get a hotel downtown and be reasy to go back to the domestic airport early in the morning for a flight to Lukla. Alternatively, local airlines offer Everest-flights where they take off from KTM and fly you up to Everest for some good pictures - weather permitting.
I have used KA's and TG's products to KTM both up front and in the back. KA upgraded their services a few months back, and are now more competitive in terms of onboard services. TG still wins, but the gap is a lot smaller now when compared to earlier this year. When coming from PVG, I would guess KA to be a more convenient option than TG.
Enjoy, and don't forget to read the details on the customs declaration form when arriving - it is hilarious!