that’s such a small difference it will barely be worth making
Could I take a 30 off my tiagra 10 spd cassette and add it to my 105 11 spd 11-28 cassette (removing 1 of the smaller sprockets)?
possibly, if you take the single 30t cog off your Tiagra, if you lose the 11 you’ll need a different lockring, if you lose something else you’ll have an annoying jump, also see above, probably not worth it
Will the 11spd chain go on the 10spd sprocket or will it just jump around horribly?
Will probably work, for a given value of ‘work’ but again, see above.
Basically it’s an awful lot of bodgefaffery for minimal if any gain.
Whack a 11-32 (or bigger) cassette on, or man up. Where do you normally ride? Road climbs in the Alps aren’t normally steep, just long….