Recommend a good tube power amp in the 100 wpc range for under $4k

As others pointed out, gain matching will be an issue. In most cases, tube amps will have higher gains that SS amps of the same power rating. Sometimes MUCH higher. This is because they use less feedback, and also the typical input tubes like 12AX7 / 12AT7 / 6SN7 / etc provide a lot of gain.

A Rogue Atlas II (or III the current one?) Magnum is a good 100W tube amp well within your budget. There aren’t too many other budget options like this without going to a no-name Chinese amp (I’m taking about stuff named like Quin-Poo or whatever, not the PrimaLunas which are good).

Your Benchmark has 3 gain settings which helps, but even its highest gain will have trouble keeping up with a 100W tube amp. It looks like the Atlas will be a couple dB hotter than Benchmark’s high gain mode (see Stereophile measurements of Atlas - and they even comment that its gain is lower than usual for a 100W tuber amp!). So you’d need to either insert an additional volume control (and calibrate by ear and/or SPL meter), or re-think your strategy.

Personally, I wouldn’t try bi-amping unless I had two of the EXACT same amp. I’ve even had two of the "same" stereo amp, but there were minor internal differences on the units (made about a year apart), and bi-amping didn’t convince me of any benefits versus running either amp alone. The very slight sonic differences between these units seemingly worked against a cohesive musical whole when bi-amp’d.

I have lots of experience with Tannoys, similar to your Fyne (I used to own Kensington SE that were also 93dB), and the Rogue Atlas did a great job powering them alone. The Rogue amps are not "typical" tube amps in that they have great bass power and dynamics with a drier midrange. So they’re really kind of like a tube amp with SS persuasions. If you went with the Rogue, I would run it full range.

I also ran those Kensingtons with 20 - 35 Watt vintage tubes amps (Heathkit, Eico), and those very much have that "classic" tube sound, but the bass response was a bit softer and I play loud so I definitely hit their clipping limits at (rare) times. I later got the Rogue Atlas (version I, non-Magnum), and I did NOT hit any limits with that amp (except once totally by accident on a Sheffield Direct-to-Disc of Firebird Suite) :)

Incidentally, I later moved on to Rogue Apollo tube monoblocks, 250 Watts/ch, and their gain is absolutely INSANE (not always a good thing with efficient speakers). I don’t think any SS amp on earth would match it. The bass response on those amps is crazy good though :)

Rogue Stereo 100 with a 93dB Tannoy or Fyne will be pretty bomb. It will give you all the bass slam and dynamics, so you shouldn’t miss that from SS :) Throw some sweet NOS small tubes in there to get a good balance of tube & SS archetypes. Rogues really respond a lot to tube rolling, and the stock tubes (other than KT120) are often mediocre.

Several years ago I auditioned the old Stereo 90 on my Kensingtons, and it was a really solid step above Atlas (at the time with EL34). But that made me so rabid for upgrade, I placed an order for Apollos instead :)

Of course the other amps you list should sound good too - I just have no experience with them. I’ve long heard Manley and Tannoy (therefore Fyne) are a particularly rockin’ combination. I should have tried them too; get slight pangs whenever I see a used pair of Snappers for sale :) There's definitely something about the EL34 sound I really like. 

I currently have a pair of VAC 200iQ and Rogue Apollo Darks (along with my solid-state Phison A2.120SE). That's an upscale analogue of the Phi 200 versus a Rogue Stereo 100. The Rogue will be more dynamic and have better bass. The VAC will be more refined smooth and sweet, especially in the midrange. Choose your preference! But I really start to miss some dynamics & slam when I go from a pair of 200iQ monos to a single 200iQ in stereo mode.

I'm not a fan of the Raven amp aesthetics (looks like a run of the mill Chinese amp to me), but I do remember that 6L6GC kind of sound (vintage Heathkits - 5881 and 7581A) sounded absolutely wonderful with my 93dB Tannoy Kensington. Classic tube sound. That kind of tube & sound in a more modern form factor (binding posts, connectors etc) with a little more power (40 - 50 Watts at least) would be hard to beat. Haven't heard the Ravens myself, but probably not a bad choice. KT88 and KT120 seem to need a lot more power and brute force behind them to sound "whole" the way those 6L6 amps do.