Brian,
An upright bass is such a specific sound... there just isn't much else like it. So far, the electric uprights I have tried left me with a somewhat neutral opinion too... the sound was okay, but for about the same amount of effort required, I can just plug in my upright. There's a Classico for sale less than 50 miles from where I'm drinking coffee this morning, and the one thing that stops me from going to play it is knowing the $15K hang tag puts it out of reach. (I should still go... just to say I did)
I haven't ever tried any of the tape-wounds on my Alembics, but I did have them on a Godin A-5 fretless once, and that was probably the closest I ever got to emulating a believable upright-ish sound from any bass guitar. And honestly, I think it was more the guitar than the strings, as I could do basically the same thing with any flats. My biggest gripe was the tape-wounds always felt either sticky or greasy... never got to a happy place with them, and eventually parted with the bass. (sometimes wish I'd kept that one)
I also have played Rick Turner's 'Renaissance' basses strung with TI AcoustiCores, and while it does come off as 'acoustic' tone, in my opinion, it's really more about how the instrument responds dynamically to how it's being played. Something about the interaction between the piezo bridge and those bronze wound nylon core strings, makes it like playing a giant classical guitar. It sorta' tricks your ears into thinking it sounds acoustic. Adding a foam mute helps, but there's still no way it passes for an upright. That isn't meant as a slap at RT or meant to say it won't work... in some ways, the Renaissance also has its own sound, with nothing quite like it. I have read of guys that strung these with tape-wounds, and swear it sounds like an upright... I remain doubtful. I imagine this is similar to the boat you're in with the Rob Allen... the sound is close enough, but the precise nature of an extreme over-build we're used to just isn't there.
Not having heard what your bluegrass/new-grass group is doing, I do get the how and the why that some might need a more 'acoustic' flavor. I can tell you firsthand, I'm doing exactly that genre' every weekend down here in Virginia. My new Custom fretless (currently strung with TI Jazz Flats) is patiently teaching me how to fit in right where it belongs. I find (unsurprisingly) favoring the neck pickup slightly about 60/40, and keeping the extreme highs rolled off, then adjusting the right hand position and attack is getting me close enough that the bass presence is felt in a positive, but not overbearing way. I call it- being passively in charge of the pocket, which of course is the bass player's job in a bluegrass group. Honestly, I think the HGB guys couldn't care less which bass I play, but they do often compliment how I sound back there when I happen to be playing the Alembics. So there's that.
All that probably isn't too helpful, but I know exactly what you mean... after playing our Alembics, nothing else feels quite the same, even very nice basses from some pretty gifted builders.
One final thought: Maybe you could retro-fit a Roland synth pickup, or something similar to one of your current Alembics and see if a blend would get you there... I know it's been done. Come to think of it - there's at least one piezo-equipped Alembic out there. Maybe a chat with Mica about that, or some other options is in order.
Safe travels home...