I owned a BAT VK-5i ages ago; did not like it. It was also hell finding 6922 tubes quiet enough to use. Each time a 5i comes up for sale I’m gob-smacked to see its ask price close to what I paid 18 years ago. I’ve owned so much wonderful gear, far superior, that depreciates like a rock off a cliff and somehow this 5i still commands good money - makes no sense to me! If looking at BAT at least go for a 6H30 model - those are great preamp tubes. 6922 are a PITA.
Had an older hybrid ARC preamp (think SP-9) in a shootout some years ago - it lost handily to every single Rogue preamp on hand (Metis, 99 Magnum, Athena). Etched and tonally lean. The Sonic Frontiers entry-level line stage fared equally poorly. The modern ARC preamps (Ref 6) are wonderful, like from a completely different world - but expensive! The Rogue Athena clobbered everything in that old shootout, and are in your price range when they come up - but the ones with the stepped attenuator aren’t the smoothest ergonomic experience.
Sometimes older VAC preamps come up in this range - probably a good option. Not sure I’m a huge fan of the modern Rogue RP-series preamps, but better than ancient ARC and BAT models.