I think you should try a combination of what serf 'rett, mavracer and RC20 have suggested.
A pair of loading blocks in the bottom of a bucket or cardboard box with 50 or 100 primed, charged cartridges set in one block and and secured from tipping or contamination by the other loading block (inverted) on top of the cartridges. If you want more cartridges, stack more pairs on top of the first. Carrying up to 500 cartridges would be possible, though 250 would be easier if you have to wade through snow.
But my choice would be (actually is what I do now) to keep my loading press (a Lee Classic Turret, just like yours) in a toolbox (25cm x 25cm x60cm or 10" x 10" x 23") with a board and "C" clamps so I can mount it to any handy surface. All my other tools (scale, powder measures, dippers, etc) fit in another toolbox. Two trips to where they are stored (one for the tools and one for the supplies) and I can be loading almost anywhere. A dropcloth beneath my work area makes cleanup very simple.
Setup takes less than 10 minutes, as does teardown and working in a warm place is, I imagine, a LOT more productive, accurate and definitely comfortable.
The difficult part, though, is figuring out a way to get your wife to suggest it.