I was recently in your predicament and the preamps I've found which have these features: Sonic Frontiers, Mark Levinson,Conrad Johnson,Audio Research,Pass labs,and Anthem.
Coincedentally, I don't think the Ref 1 has processor bypass, instead I believe it has another tape loop.
The Sonic Frontiers 3 won't keep up with LS16. You'll need to go to LS25 or Ref 2 for tubes to best it. The LS25 doesn't sound much different than the LS16. I am yet to hear the LS25 mkII. The Pass Labs preamps are very clean. If you have the dough, and like your LS16, go ARC Ref 2.
I recently purchased the LS16 to go with my Lexicon MC1 and am currently very happy.