My decade-old Boss GT-8 does delay and reverb tails between patches, but it's a nighmare to set up; a classy alternative that isn't a nightmare to implement is a boosted Solo setting for each amp patch that works nicely. I would think the easiest and best solution on the Helix would be to add a boost and/or an alternate amp into whatever patches you plan to solo from, so your tails would be intact when you switch those bits off.
As someone who owns a boogie rectifier, I can say with certainty this post is proof that Line6 did not model the exact knobs and knob behavior of a boogie rectifier. Anyone that has read a rectifier manual will tell you that A) there is no "Drive" knob, and that B) diming the Gain results in unusable garbage. Mesa amps are tricky to get really great tone out of because the knobs all impact the tone differently than on, say Marshall or Fender amps, due to how Mesas are wired. This is not a criticism of Helix designers; good on 'em if they've made it easy to dial in great Recto tone. Just calling out some marketing nonsense.
Thanks, bieb, for the first impressions. It sounds like your usage scenario is pretty similar to how I'll mostly be using it. Really excited about this!