Take a peek at these routes - there are about 5 for Stelvio, all starting and ending in Livigno (which is decent place to stop when in the area) but obviously asy to edit to suit your chosen location.
https://www.myrouteapp.com/profile/routes/485#981738/name/asc
With 2 days to get there - A mainly motorway & LONG day one will get you to the Black Forest (but if you can travel down to the Tunnel the night before, or even better to get across to the French side it's much easier) from there to Livigno you can mainly use nice roads.
3 days each way allows for no more than the first morning being Motorway - and you can ride through many nice places on pleasant roads on the way, but would leave you bugger all time once there, so I would stick with 2 days each way, and let the boredom of the Motorway "buy" you an extra 2 days once there....
....Leaving you 3 whole days to ride all the other great passes in the area - Fluella, Albula, Gavia, Splugen, Bernina, Maloja and Julia are all well wroth riding...
...also means you are not pinning your hopes on that one day you have being nice - with 3 days you would be unlucky not to get a nice day at the top of the Stelvio, with just one day there is probably a 1/3 chance it will be crap - or even blocked due to snow which can happen on any day of the year, we went early August once and arrived at lunchtime, got a great ride up to the top with snow at roadside - that morning it had been closed due to overnight snowfall.
With another 2 days you could come in via Andermatt and have 2 nights there and ride the famous figure 8 loop - easily done in a day, and Andermatt is easily reachable in 2 days from Calais - and the ride from Andermatt to Livigno is fantastic, and fairly easy day if you go fairly directly - or go via the Lukmanier, San Bernadino, Splugen and Maloja...
https://www.myrouteapp.com/route/open/908030
Look at google Images for Splugen - really stunning!