OK, went and ordered step-down adhesive heat-shrink connectors. This would be vastly more convenient if a store actually carried these things somewhere... I wasn't real happy with the state of affairs though and will glady wait til they arrive to rectify the situation.
Not sure how conduit in the mast would provide support? It would prevent movement, but you'd still have the wires hanging straight down the conduit.
The tricky part with my mast is it has been chopped in half for a mast repair, and has an inner sleeve at spreader-height. I'd have to de-rivet the top cap and try to get something lined up midway, and most likely also have to unscrew and rip the mast in half again, to do a proper conduit at both sides of the repair.