Split board!
Have you walked any reasonable distance in snow shoes before? I find them slow and not very efficient. The walk ins in Scotland can be looooooonnnng compared to the plodding our north american cousins often enjoy. My first few outings on snow shoes were in Canada and I rarely seemed to be in them for more than a couple of hours (although, in saying that, we never strayed to far from resort). In the Cairngorms in particular, so much of the walk in can be skiied/split boarded.
In the past i’ve strapped snowboard boots to my pack and walked in with regular mountaineering kit (Nepal Extremes + crampons + axes). More weight obviously, but as you’ve pointed out, moving up a slope in snowboard boots is a nightmare.
Split boarding is definitely the way to go, but it’s pretty expensive kit, worth seeing if you can hire some?