Two other supply options stand out.  Using a lot cost switch mode bench supply module, or using lipo batteries.

Bench supply module

A range of bench supply modules are on the market which could be used.  They have an LCD and interface for setting voltage and current.  Having a constant current mode is the biggest thing going for it as one doesn't need to worry about the voltage when changing wire lengths.  Just set the current for that gauge/resistance of wire, and it'll adjust voltage for whatever length of wire is used.

This one should be plenty  capable, able to supply 15A and up to 50V.

The big catch with these modules is that not only do you need the module, you need an AC-DC supply to power them.  Add on a 300w+ 48VDC supply, and that $50 isn't so low, and it is getting pretty sizable.  One could probably get away with an unrelated supply from a transformer, rectifier and cap, though I don't think I have an appropriate transformer.  I believe I do have a AC-DC supply that could work, but this is getting quite large and is a bit more spendy on top of still needing to do all the mechanics.

Li-po supply

One of the advantage of hobby li-po batteries is they can supply a lot of current for relatively low cost.  A brushed motor ESC and a servo tester to drive it ensure it can even regulate the power.  This makes for a portable setup, even capable of putting it all on the bow itself so there is no lead to it.

The downsides are that it requires charging in advance, the power will dip as the battery drains requiring adjustments between cuts, and it would still need a voltage/current display.

I do have suitable batteries, though I don't have a brushed ESC or servo tester, so I'd need to purchase those.