I suspect you are going to be disappointed with the speed (and effort) required using a hand crank winch. It's one thing if you are only pulling something 3 or 4 meters. Since you are trying to stay away from gas-powered equipment and appear to be looking for lower-budget items, I'm guessing a tractor 3 point hitch mounted logging winch is out of the question.
I'm not a fan of using a vehicle mounted electric winch for any significant, regular use for logging: the winches are slow (especially under load), and the duty cycle is generally very low (requires frequent stopping to let the winch cool). A longer winching session (winching out multiple logs over any significant distance) also puts quite a strain on the vehicle's electrical system and battery. Most vehicle charging systems will not keep up with the drain of an electric winch used repeatedly in quick succession. They are great for a quick recovery of a stuck vehicle or pulling a downed tree out of the road. They are not so good at extended pulling.
I recommend going to a capstan winch. The best I have seen of these are those made by
Portable Winch Company. I have used their gas winch models and been very impressed. I have not used their battery model (
PCW3000-Li), but have spoken with two people who own them and use them for gathering firewood and clearing storm damage. They are happy with them, but did note that you are not going to get anywhere near all-day use out of a single battery. I know this is a different battery system that what you already have, but it's worth it, and Dewalt makes nothing even remotely similar. On the upside: the PCW3000-Li uses Greenworks 80/82V batteries (which are also the same style used by some other cordless tool companies (Briggs & Stratton/Snapper XD, Cramer, Stiga, and Kobalt), so you do have some other sources.
A couple of notes:
when comparing the useful work you can get out of the batteries available with various brands, it's important to note that looking at just the Amp-Hour rating of the battery is only half the story. You need to compare Watt-Hours, which is just Amp-Hours X volts. a 40 volt 4AH battery can do only half as much work as an 80 volt 4AH battery.
The weight of the log is only one factor that goes into determining the amount of pull required to move it. A 1000# log may take far more or far less than 1000# of pull to move it. Terrain, the shape of the object, they type of soil, & etc are all factors. You can significantly reduce the amount of pull required by using a skidding cone (PCW also sells these - see their Forestry Accessory package). Even shaping the end of the log to taper the edges and trimming limbs/stubs so they don't dig in as much can make a noticeable difference.