You could try that, but there is no standard for ring heights, shimming scopes can be tricky and can potentially damage your scope if not done correctly. There is probably a medium ring out there that's a touch taller than yours. Measure yours and look around for something a bit taller.
A med 1” BKL is actually pretty high and should accommodate your 44mm objective.Dovetail Centerpoint and UTG/Leapers mounts seem identical to Sportsmatch in height and not as high as their BKL counterparts.Mine (the BKL), on a 2400KT Crosman, had a Hawke 4-12x50 AO and it was able to accommodate it, although the barrel on this AG is lower than the breech by approximately 3mm.