Winch problem

We recently re-commissioned a winch that had been operated successfully
for years using armored tow-target cable. That being difficult to find
these days, we are using regular stranded cable and are having trouble with
the cable piling up at the center (width-wise)of the drum, then slipping off
to the side causing slack loops of cable that eventually grow enough to whip
out beyond the circumference of the drum, impacting adjacent structure. The
winch has never had a level-wind mechanism.
It would seem that the stranded cable has less tendency than the smooth,
armored cable to slip off of the high spot at the center of the drum and lay
into the lower, edge areas of the drum, which would result in a more level
winding of the cable on the drum.
It looks like a level-wind will be necessary, or a return to the old
armored cable.
Any suggestions?

Lach Ohman