If the frame, axle, springs and wheels are a in good condition (that is, require nothing more than a bit of paint and a new set of bearings) my assumption would be that the trailer is salvageable / can be improved and that doing so is worthwhile. (The bent winch post should be replaced, but as you note, it's a separate piece).
When I got my trailer (a '64 model year), it developed a frozen wheel bearing after a week, at which point I took the boat off of it and rebuilt it. New set of bearings, addition of bearing buddies, scraping rust and repainting. I replaced the wooden boards of the bunks by wider and longer ones (could have made them even wider and longer, actually).
About 10 years later, I needed to repeat the paint job (the trailer sees saltwater occasionally), and redo the bunks again.
Here's a picture of the trailer ready to retrieve the boat.

- Trailer ready to receive boat
- Trailer.jpg (76.03 KiB) Viewed 14944 times
You can see my trailer has the traditional center rollers with bunks. (Some people go so far as to use only bunks). I park it with the rearmost roller right at or below the water surface. I replaced the original roller with one that's a bit wider and has a shallow V shape with a central notch. I trap the bow in that notch. Then, when I pull the boat up the notch acts like a pivot, helping to align the boat.
The rearmost roller is dropped an inch or two, so after a while, the boat begins to rest mainly on the bunks (with no weight on that roller), with only the bow continuing along the rollers. One of the middle ones is positioned below the centerboard and prevents that from dropping during transport and launch. With this setup, I've not had any trouble getting the boat on the trailer straight. If for any reason it's off by a bit, I usually just lift the back and shove it over. (Even partially supporting the rear by lifting will reduce friction and allow it to slide. I don't think you actually have to lift a full half of the boat's weight.)
In your case, just shove the boat over a bit until it's fully centered. (Until you replace the winch post, you may need to do that, even if you reposition bunks, rollers as suggested).
Your bunks should be adjustable, as should be the rollers. It's not hard to make them conform better to the boat, but the bunks should probably also be rebuilt: new wider boards screwed on and new carpet padding. The latter need occasional attention so they roll freely.
For the winch, remove the wire, take any rust of, spray with Rustoleum and grease the moving part. Then get Amsteel 3/16" and use that to replace the winch cable. You'll need some extra length (about 12") for splicing onto the shackle, but the good news is that splicing Amsteel is super easy. No need to replace the winch itself unless it is so rusted that a critical part is below strength. (In case you are wondering, Amsteel has the same strength as wire of the same diameter; 3/16" gives you additional reserve against chafing or aging. It should be strong enough to lift boat trailer and car, just about, but is it so much nicer to handle than wire).
(Just looked at your post again and you write "winch rope" - if yours already uses rope, forget the comments about wire, just replace by Amsteel).
You should be able to push the boat to where it's aligned to the supports (and you should be able to unbolt and raise/angle even the existing bunks to where the meet the hull, and preferably take more of the weight in back than the rear roller(s)). If you need to lift the boat a few inches while working on the trailer, a 2x4 or 2x6 will make a handy lever; you can use a suitable frame part to use as fulcrum and lever up the hull where you need to, then insert some blocks to suspend it at the new height so you can do things like raise bunks.
The DS is heavy, but it can still be manhandled. A helper is nice but much can be done even by one person.
Once your DS is aligned on the trailer, I see no reason why you can't work from the inside.