I agree, your best hope for a quiet tube amp with 250uV input would be a high transconductance triode. Unfortunately they are usually touchy - unstable with high grid impedance, they often suffer low-frequency noise and random drift, and the tight grid-cathode spacing amplifies sensitivity to microphonics. At radio and VHF frequencies, the best tubes are quieter than the best solid-state devices, but in practice at audio frequencies it's usually the other way around.
Incidentally, the Repro and other tape preamps of ours have no high-treble equalization - it's not needed with a wideband tape head at 15ips. But at cassette speeds, the necessary head gap becomes smaller in proportion to the speed, which also reduces the available output (along with the narrower track). So there is a good chance the the head gap is more of a compromise, and some HF boost could be needed.