I was very surprised to discover how reasonable the price of Amsteel synthetic line is. It's actually less expensive than traditional braided rope OR wire. If you've got your mast down anyway, you might take a look at it.
One distraction was the thickness - I had been casually looking at the price of 3/8" or 7/16" synthetic, the size of the existing rope when 3/16" is more than strong enough, the same size as wire. 0.63/foot at Defender the other day.
The other distraction was the need to accommodate the winch and rope clutch, either with new hardware or with some kind of splice or cover to thicken the line for handling comfort. With the reel, designed for an all-wire halyard, you don't need either, despite them being "out of repute" as Christian says.
I agree that reels are miserable for daily sailing operation but there are tons of worse mechanisms on boats for once-a-year operations. Getting into the lazarette to fog the engine for the winter? Sux. Disconnecting hoses to winterize the head? Sux. Spinning the handles on cradle/jack stands to accommodate the hull shape? Sux. Climbing the mast to replace blown bulbs and bent Windices? Sux. etc.