Pics would help to determine exactly what you are dealing with. Edit, ok, now I see the pics. I think my solution below will get you great results on the suspension ect, still can't tell on the chassis.
I've been asked that question many times because I'm a huge fan of having a bare clean chassis and to show it off.
More times than not, it's not undercoat but 40 years of grime that appears to be undercoat.
First determine what exactly you have. If you can use slight heat to a section, and peel some off like a sticker, then yes, it's undercoat and heat and scrape is a starting point, but you likely won't be happy with the effort vs reward.
If you can "clean" it to the bare paint, then the job will have much better results but won't be much easier.
What I do is buy 4-5 bottles of orange glow type cleaner. I have heard that wd-40 works better but have yet to try that.
I presoak everything with multiple applications a few hours before the messy part.
Then I drive the car to my favorite hot water quarter do it yourself wash, I pick a not busy time.
I dress i with googles worst cloths ect and for about 20-30 dollars in quarters lay on my back and go to town. It's not a fun experience but is very rewarding once the original painted chassis shines through.
This is the only picture I have to show the after... this was after round one, it's better now.
When I got this car, I thought it had undercoat because everything was uniformly black.
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