I'm feeling something here...
Brad (for those who don't know him) has many great pieces of gear, has lots of experience, and a trusted set of ears. He knows what multi-band compression is and he knows what it does and how different versions do it. I'm sure he even owns several devices which can do it right out of the box.
Now, I think I might have a clue as to what he's wanting to hear sonically, but I'm by no means certain that he's for sure on the right track in describing what the technical requirement is. Only if we can quantify the effect and result correctly can we build a simulator or tool, whether the issue is digital or analog. (Following on from my recent comments on the EQ 'ping' device....)
Anyhow...
I'm not altogether certain that envelope transience is the thing. A compressor looks at the envelope and not the instantaneous waveform. A transformer deals with the instantaneous waveform and its rate of change, and is a magnetic device rather like tape. It has reluctance, remnance, permeability, and a number of other properties that tape has, though these are exploited and employed in a rather different way.
Of course, the best 'effects' devices (and I prefer to think of what I understand Brad to be searching for as an 'effect') have a way to control the amount of the effect.
I don't see that the non envelope-dynamically-related (i.e. compression based) suggestions so far have any way to govern or control the amount of the effect.
-So I don't have a way to get what I think Brad is looking for, but here are some "backward-thinking" ideas:
Brad, since the effect of tape "sound" was something that engineers always wanted to get rid of in days of yore, perhaps we should think of other things that were adjusted to proveide softening and under-performing. Something as simple as a couple of sets of Dolby 'A' units, with some sort of nonlinearity between them would induce dynamically -related softening of the signal. Dolby 361's had all-discrete class-A circuitry, with very nice transformers on them on both input and output. If you fire a signal into one, encode, decode with the other, and in between, load down the signal with a variable resistance directly across the signal lines it would provide a way to increase the load on the transformers ('bending the sound in an analog way) and also the slight level change would start to soften the HF progressively and mand-specifically, due to the way Dolby 'A' works.
Since 361's and 360's are so darned cheap on eBay at the moment, I'd seriously consider playing with this. -If it's not what you want, you can either use the 1RU cases for something else, score some serious transformers, or sell them on eBay again... they usually go for about $50 per channel if you hang around for a bit.
I just installed 72 of the darned things in a rack. I only used MH-type and SP type for multitrack 'A' type use before now, and I hated their clipping behaviour, but I assure you that the 361s are a different beast entirely. -Since the experiment involves no internal modification, you might even borrow a stereo pair and cascade them in mono to see if the effect is any use, with no internal modification at all...
Whaddayathink, Brad?
Keith