To paint or not to paint the underside

Soooo, my Duster is in pieces and has not run for almost 7 years. Until this last summer, it was in non-climate controlled storage for the previous 4 years. It's home now and I am beginning the process of putting it back together. I pretty much have all the mechanical pieces that I need on hand so that part just a matter of making the time to complete the individual jobs. My hope is that I can work on it regularly over the winter and have it ready sometime in the spring/early summer.

With most everything stripped off, it's easy to see how crusty it is. Having it sit uncovered in a non-climate controlled garage took it's toll, there is a good amount of surface rust. And to be honest, I've never liked working underneath this car. The undercoating scrapes your hands, there's tons of grime, it's just nasty. The engine bay has seen better days as well. the paint is discolored and oxidized, there's extra holes, chemical splatters and lots of grime.

Cleaning up and painting the underside would make it way more pleasant to work on. The engine bay would really benefit from a fresh paint job. If I'm gonna do these two things, now would be the time.

Believe I have a few options. Number one, I could strip the underside myself with a torch and scraper/wire wheel. That's tedious and messy and I doubt I'd be able to get every nook and cranny as clean as I'd like. It's cheap though and I could do it while the car is on the lift.

Number two, there is a place relatively near me that does a lot of old car media blasting. They would make quick work of the job and it would likely be cleaner than I could ever get it and keep my shop clean too. Drawbacks would be a higher cost and the difficulty of transporting the car on a dolly of some sort. Neither of those things are a deal breaker by any stretch.

The problem(s) with the latter method is that I would probably need to remove everything from the chassis. Not a huge deal, it's mostly there already but I'd have to take off the bumpers and whatever is left in the engine bay so I would be adding a little extra work on the back end to put that all back on.

I also keep looking at the ancient frame connectors and wondering if I should cut them out and get the ones from USCT. I used those recently in my '68 Coronet, nice pieces. That would be a big job in and of itself though. I can weld new ones in myself but I don't have a rotisserie so it would all be overhead which increases the degree of difficulty. It would help to get things cleaner for sure, can't really get at places the connectors are covering up. They're only 2x3 tubing so it wouldn't be a total loss.

Last part about media blasting is how far to go. Not sure how well things can be taped off to prevent damaging the paint on the body. I definitely don't want to paint the entire car, too much money and time, I'd never get the damn thing done. But, there is no paint left on the undersides of the rockers so it would be good to re-do those areas to prevent any further oxidation.

The exterior paint is definitely not perfect. It's been repainted in spots. Seems like it could have been in a minor fender bender or two. I see a repair on the bottom of the passenger door that I hadn't noticed before and some paint drips in the engine bay. It's a 100% solid car though just needs some cosmetic love. But again, I don't want to get involved with painting the entire car, it will never get done.

Also, I'm not sure what to use underneath if it gets stripped. Spray bomb? Real body paint? Truck bed coating? I really don't know. Obviously the engine bay would be EV2 body paint but from what I know painting an engine bay can be a little more forgiving than a full body job. Either way I have a friend who is an ace body man who could do it so I'm covered on that end.

So do I go for it and clean it up or leave the ugly on and just get it running? Appreciate everyone's thoughts and insights.
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