Territorially challenged?
Are you growing 'em up a trellis or strung like tomatoes on a string, or just crawling along the gound? Seems to me you must be growing them in the open, and allowing thenm free range?
You could encourage shorter bushier growth if ya let laterals form by nipping the growing point out early in the season.
I don't think there'd be much point in growing them like spuds in tyres, 'cos spuds need to be moulded up, which is sorta what ya do when grpwing a spud in a tyre and add a new tyre full of soil as the haulm grows.
Cukes and gherkins do not need moulding-up but their habit is like pumpkin and marrow, putting rootlets out from the nodes into the ground if not trained up a support, thereby supplying extra nutrients to the vine's new fruit as it developes.
Maybe you could organise a series of rich compost pockets in a row, and
allow MAKEthe vine grow along the row,
making LETTING it's new rootlets "take" in the compost pockets, a point for extra watering and feeding?
Perhaps you could "espalier" the vine by twisting it round the wires in a fence structure, keeping it off the ground?