Polytones are not known for their bright Charlie Christian-esque/Grant Green-esque tone.
Those guys used tube amps.
Besides sufficient power in a small portable box Polytones are known for the their 3-position Treble/Bright/Cut switch.
As I recall the middle position is Normal.
Upper position is Bright.
And lower position, the one that most jazz guys use on the PT because the other two positions have a harshness to the top end, is Dark.
If you've ever tried to play pop or R&B rhythm guitar styles through a Polytone you'll know what I mean about the quality of its top-end.
It sucks.
Joe Pass used a Polytone for several years and was getting a quite dark tone at the time.
Most guys like them because it's easy to cop a Jim Hall-type tone from them.
If there's any player in jazz who influenced the dark-dry jazz guitar tone it's Jim Hall. (He used tube amps most of the time, but was using a Walter Woods ss amp in the 70s and 80s and he may have dabbled with PT's as well.)
I always thought of that dark jazz guitar tone (which I am *very* fond of myself although I can sympathize with folks who don't like it) as being part of that whole 'cool' school of jazz where flamboyance was shunned for the sake of content expression and understatement.
Singers and horn players were using little or no vibrato.
Big bands were paired down into small ensembles.
Understatement was a desired characteristic of the music.
Pat Metheny and Mick Goodrick were both using Acoustic 134 ss amp models just before the PT's came out in the late 70s.
They had similar design goals to the PTs but were in a larger enclosure (4 X 10 open back combo shell) and weren't as portable.
Metheny kept using the guts of the 134 for as long as he could before it disintegrated.
I think Pat liked the 135 because it reminded him of his old Standel, a ss amp that Wes used to play as well.
The fact is though that the tones they liked to play with are just as easy to get through tube amps, but only at lower volumes.
The main reasons not to use a tube amp for this type of music, especially when it starts getting louder, is headroom.
Only tube amps with 4 6L6s (or similarly powerful power sections) can hope to stay clean enough at louder volumes when playing through them with a dark sound, and those amps tend to be quite a bit heavier than a ss amp with similar or better wattage/headroom characteristics.
Most jazz guys don't want to lug around heavy amps.
In the Axe, these considerations are irrelevant.
Most of the amp sims of clean tube amps can get as loud as you'll ever need, assuming that you're monitoring the Axe with something that has 100 watts or more of clean power available.
(Although for some reason the USA Clean sim seems to be capable of significantly greater relative levels of 100% clean tone before it clips the Axe's digital output leds compared to the other clean amp sims.)
So I tend to gravitate to the USA Clean sim or the Double Verb sim for my jazz tones in the Axe.
But a real Twin (and even the Mesa MKIV) would have a hard time staying clean at the levels that I often play at with loud drummers.
And if I was trying to peg the sound of a Polytone, for some reason, I wouldn't use an Amp Block at all.
I'd use a PEQ and I'd use its Level parameter just like the Level Parameter of an amp block.