First off, it’s a
windlass. The word you’re using repeatedly is for a
weather condition of no
wind.
Now that’s off my chest, let’s talk about your windlass. As another poster has mentioned, the gypsy for handling chain will often handle correctly-sized 3-strand line, as long as there is some but not too much tension in the rode so that the rope is jammed into the teeth of the gypsy enough that it doesn’t slip.
Lots of people use vertical windlasses with mixed rodes, so if your rope rode doesn’t
work with the gypsy then maybe you need new rope. It sounds like your rope rode has been lying around for years and has likely gotten very stiff (and
lost some strength). Try a short length of new 3-strand rope with the gypsy and if it holds as it should then go ahead and buy however much rope you think you’ll need. If the short length doesn’t
work, your gypsy may be one that doesn’t handle rope well. Bummer.
The upper part of the windlass is called the drum and is used for handling lines, usually for
mooring or halyards, not anchor rode. You’ll notice that a line on the drum does not feed into the hausepipe. Unless you have a rope-only rode you should not need to use the drum for the rode when raising the anchor.
However, if your gypsy is not handling the rope very well (I assume it slips?) then you could move it to the drum and use 2 or 3 wraps. When using the drum you will need to hold the tail in tension, otherwise the line will slip on the drum. You will need to be diligent in feeding the trailing end through the hausepipe - maybe a second person will be needed.
When you get to the rope to chain splice, you will need to stop the rode, secure the chain with a chain hook or similar to take the tension off the windlass, then take the rope off the drum and lead it around the gypsy, then start to
lift the rode again. Hopefully the rope will not slip much during that short period until the gypsy picks up the chain.