For what it's worth, I've never done the conversion you are proposing.
However, in Australia
I am a licensed motor
vehicle ( usually taxis) LPG (to you ..propane) installer. We convert cars from gasoline fuel
to propane. Despite having plenty of qualified experience, never ever would I bother to convert an alcohol stove
to propane. Not impossible, but I'd be eating and drinking cold things before I'd even think about this conversion.
Maybe in your part of the world conversion specialists exist and I hope they do.
But frankly, as already suggested, I'd somehow try to find the money
for a new propane stove.
Good luck which ever way you go.