Transistor Preamp that sounds like a Tube Preamp?

1&1: easy, just attenuate over 8kHz
2: easy with SS -- but difficult to achieve with above & below. You just need high frequency extension
3: Dunno probably 1&1 above.
4: A US made product. The Euro has reached $1,55.

Seriously, while you'll get all the usual "my pre is like that" type of response, no SS pre emulates tubes at that price level. One I know of that comes somewhat close is a Symphonic Line -- but it's more expensive. Another is the older big Rowland.

Really, why not just buy a tube: they're usually cheaper for what you get in terms of sound. Good SS pre's are miserably expensive.

My goal with this thread was to see if SS technology has advanced to the point that it was able to overcome these limitations.

Well, circuit design hasn't really advanced much... and that more or less cooks the issue. We do have good quality materials though, very expensive however, and rarely used in hifi equip. Lastly, strong points for a "very good" ss would be transparency & bandwidth & some homogeneity in signal amplification; not quite your stated cup of tea but your description does not really fit SS you know!
Sooooo & however & IMO &etc etc, you might try an ancient MLevinson pre (the ML series) or a Cello "palette" or an '90s accuphase, or an old series ('80s-;90s) Goldmund. Not easy to find, I know, but better performers than many of the new stuff @ your price point.
You also give the ones mentioned above a try: Ayre is easier to find than an old Goldmund, but a super performing Ayre is more expensive (new) than a used Goldmund, of course! Regards