I agree with Steve and would add, rope with a twisted strand always needs to be coiled in the same way to provide a memory, bit like stowing a hose, it goes away better if the hose goes away with the same twist or same handed person doing the retrieving. Discipline when putting the rope back in the locker is the key, whenever I have put it away badly in a choppy sea I nearly always have a loop that forms under the deck when releasing. Time consuming and tiresome but necessary. If the rope is stowed correctly it should look like a polo mint from above, then the chain can drop in the middle.
Most boats up to 7.5 mtr boats with vee lockers are not suited to the deep anchoring we do, therefore the rope does not have enough drop to coil itself as it comes in off the gypsy, hence we hand stow, especially a horizontal gypsy which the majority are.
The vertically dropping rope off a vertical gypsy stows better in small lockers. I fitted one on my last boat it was much better and the motor is not in the way either.
I coil the rope in the same way Steve does, where the rope is tied off to the bollard that is always slightly troublesome as it has been twisted. Plait has less memory and therefore better, but some gypsies do not like plait because it reduces in width as it stretches so gripping it can be an issues at full load, make sure it is compatible with your gypsy before purchase.
I use nylon 3 strand and it is fine, poly is a poorer quality generally and used by commercial fisherman on pots etc and not as good for our type of use.
I was listening to your troubles out at sea, seems like you were very unlucky, a string of loose pots or nets maybe to have drifted so far, it would not matter if you had tripped your anchor with cable ties in that situation. I tend to turn my rope around after a couple of years to give it even wear.
I am sure you know all this Ben, the answer is for those members reading and taking on advice. The next choice is what type or pattern of anchor and how much chain.