The main problem with your question is that your goal is individually subjective.
As has been stated ad-nauseum in these hallowed halls, processing is a bit of a voodoo science. Go back some years beyond your target and you'd find that some of the most "interesting" sounding stations had processing systems that were securely locked away from pretty much everyone but the guy who built it. Those systems were collections of various crossovers, mixers, compressors and limiters, modified and wired together to develop that "signature" sound that many of us old-timers remember from the early rock years.
Why were these "wall-of-sound" generators so popular in the analog days? It wasn't for their sonic clarity, that's for sure. They were designed, to one degree or another, to make the monitor needle play dead at 100%.
Would such a system sound as good today as you fondly remember from 30 years back? I doubt it. Back then, the people who are really good at this were just figuring out how to take that cludge of glued-together pieces, replicate that sound in a single box and, hopefully, bring some semblance of quality back to the dial. The single-band VCA processors that Kelly alluded to slowly fell by the wayside, partly because of that wideband "pump' that you're talking about. Getting that is not much of a secret. Buy a used version of what Kelly suggested... or a single-band Symetrix comp-limiter... or even an old LA-3, and you'll get all the pump your heart desires.
In that section of time that I come from, my heart fondly remembers the Frese Audio Pilot as a ground-breaking processor. This was around the time that CBS was marketing their Audimax-Volumax combo... and some time before the advent of the Dorrough 3-bander. We were, for the most part, still trying to get the most bang out of single-band comp-limiters, and the Frese box certainly did that, warping transformers and seriously shortening the life of modulator tubes in the process. On the other hand, you'd be hard pressed to find anything louder on the dial. On the AM side, there was a running speculation that George's box played a part in motivating the FCC to establish the 125% positive limit. Given enough extra iron and glass, I recall hearing numbers suggesting the 200-300% range, or even higher, might have been possible... though it took a guy like George to make that happen. There are stories that some of his gear was used in a couple of Mexican border-blasters. But, it was more likely that you'd find his box on the front end of a Bauer 707 or a Gates BC-5P... transmitters that were hard pressed to hold 100% over time. Watching those rigs light up was entertaining and, maybe just a little scary.
Over here, there's an informal effort to get one of those processors going and try it on a modern station. it would need to have a NRSC filter fitted to it, and the builder once suggested it couldn't be practically reined in to the 125% limit. Given that, and the sorry state of our current receivers, would this box sound like I fondly recall? Probably not. It would be loud enough... maybe... but given how modern processors develop their "loudness quotient", I'm afraid the AP would pump badly, with a fairly horrible grunge to it... given it was only a single-bander and included very aggressive, non-"distortion cancelled" clipping.
My point is that the sound you're looking for is likely only in your head. How you get it will be difficult for anyone here to suggest, because the combinations are endless... probably no single box will do it for you, and none of us can hear the sound that currently resides between your ears. You'll know it when you hear it, but your description is a common one and most of us probably recall something more-or-less different.
Good luck though. You're certainly not the first to go down this road.
