I find the time delay between the direct vocal arrival and the reinforcement from the PA a difficult thing to compensate for.
If it wasn't for that aspect I'd suggest simply EQing it with a healthy presence range boost and possibly a bit of an upper-bass/lower-mid scoop if it's vocal recital only without music behind it. If accompanied, I'd probably try a similar strategy with a milder curve to balance the benifit to the vocal against any detrimental effect on the music. That can help speech clarity and intelligibility directly from a tonal perspective, and partly compensate for excess room 'verb even though it does nothing to actually reduce the level of it. But that no news to you guys I’m sure.
EQ doesn't do anything for the difficult 'slapback echo' problem though. I frequently encounter that with classical material in a particular hall with spoken segments before the piece by the composer, conductor, or performer who are typically standing 10' away from where I sit, while the PA speakers are behind them something like 50' away, soffit mounted high in the wall behind the stage. Fortunately it only affects the spoken segments since the performances are usually fully acoustic or occasionally for things like Steve Reich pieces, visiting amplified ensembles or electronic organ material they'll place mobile PA speakers on-stage about equidistant with the acoustic sources. Farther back in the audience the direct sound of their speach is probably attenuated enough so that the PA dominates and the problem is not apparent for most patrons.
A ‘de-slap / de-verb’ algorithm would be something of a golden for live recording egg if it worked transparently enough. The tools in Rx you mention come to mind and have intrigued me, but I’ve never tried them and suspected that they just weren’t clean enough to be of much use for music (if perhaps quite useful for something like forensic audio).
If any of you guys find one that does works decently for music, please let me know.