A 4% slope would make for a long ride to get to everest elevation... like 400km I'd guess... There's an everesting calculator out there you can plug strava segments into and it'll tell you how long the ride will take and all that jazz, fun to play around with.
I think my carbon roadie is lighter than any of the single speed bikes I have. Probably better to just make a 1x hill-climb bike with a really light corncob cassette on the back and a smaller chainring. Could just run one brake up front and use downtube shifters if one were building a specific bike for everesting I'd go with something like that in theory. Run a superlight tubular wheelset too and all that other weight weenie kind of stuff.