Is it just the keys that are sticky, as in to the touch, or is the actual movement sticky?
Something like ISO alcohol? Something that's going to evaporate off and not leave a residue that might potentially short something.
Best bet is to just take an old lego block or such, get it in the same sticky state, and see if repeat rinses with ISO would clean it off.
Disclaimer, i have no idea if this would work or if it will damage the keyboard, just throwing around an idea

In my uneducated opinion it could work, but the big issue would be how the cloth material would fare. Although i guess it could hardly come out worse off than saturated in sugar.