Do you think that one could somehow compensate for the different weights by slightly reducing the horizontal width of the characters while increasing the tracking? ... or would that be a stupid idea?
Yeah, that doesn't really work, sadly.
So I've found that if you use Monotype Grotesque Display Bold Condensed for the body text, it's pretty close to the shape, weight, and metrics of the original sign. However, that font is missing certain key character shapes that are so obvious in Agel. So I manually replaced those characters with their equivalents from Headline Bold. And that looks pretty good.
Obviously mixing typefaces is not something they would have done for the original sign. So perhaps the digitization of Monotype Grotesque eliminated some of those features? Or Headline Bold was lighter in its original form? Maybe they used a different, third font?
Without a Monotype hot metal type catalogue it's hard to know for sure.