Relocating the PVC from behind dishwasher
Yeah, a handy DIY person could do the re-routing of those hot and cold water line connections. You would have to deal with shutting off the water supply, cutting out all the old stuff and then re-plumbing in with new piping and fittings. Hopefully you get all the parts that you would need in one initial trip to the big box store. Do be aware as you get ready to re-route the pipes as close to the wall and as low as possible you may be faced with that electrical box back there being in the way.

After all that the quote really does not sound so bad considering the nature of today's prices for things. But it is totally doable if you have the gumption and determination to see it through. It may even be the occasion to acquire some new tools!!