My idea is something like this:

The black represents armor, and the gray represents internals. Both would have colors, getting more red as they weaken (like the paper dolls), and the armor bars & internal bars would function independent of one another. Undamaged sections are green.
Now, since I'm bad at explaining, I'll give an example instead.
Let's say I'm in a Jenner-D. This is my mech's current paper doll - I've been kicked around pretty good.

When you filter out the transparency and such from the colors, you end up with something like this:

In the heat of battle, I usually find that looking at the color doesn't really indicate much, especially when the entire mech is roughly the same color. All I get is it's either meh or about to fall off. For example: the "yellows" in that image are very much orange- I put a swatch of actual yellow next to a swatch from the arm armor for comparison.
Now, for the sake of the example, let's say my left arm hasn't taken any damage, and my right arm has some internal damage, I guess from overriding a heat shutdown or something.

hurr I'm so good at photo manipulation
Again, filtered to just pure color:

Now, with the HP layout I used above, this would correlate to:

something along those general lines. (It's not exact, I don't know the exact relation between color and HP percentage or anything, this is just a mockup.)
This is roughly what they would look like in place of the paper doll:

And a variant with the blacks replaced by white for more visibility:

Now, obviously I'm not a graphic designer, and let's not mince words here, these mockups are pretty god-awful. Don't judge by art quality- if PGI was to do something like this, they'd obviously make it a lot better than mine. It's the concept I'm looking for feedback on.