If you were using USB to connect to the amp, I’d say the H390 might be worth a try because it allows to control volume of the amp through USB. See here:
However, this is just about convenience and not about sound quality. Considering the price range you intend to invest in new speakers, I think you might gain more by buying an H190 and spend the remaining money on even better speakers. In my opinion, spending more money on the amp than on the speakers is usually not beneficial, meaning the H390 would be overkill for speakers around $4k a pair.