Being in the UK, I'd initially have suggested one of the 'BBC derived' family of speakers, current examples of which usually offer great natural midrange timbres at least and a good perceived soundfield as pair matching is pretty good. Prices are now silly-high on almost all of them, as their markets will happily pay this money it appears. For used ones, Harbeth SHL5s or C7s from the noughties might be obtainable used for around this figure but as they sold for more in the US than in the UK, this may not apply and both these have the kind of gentler perceived balance the HD600's have (from memory).
I don't know current KEFs, but the Meta ones seem slightly 'calmer' in the mid high frequencies and this may push the listener's attention back to the midrange a bit more. I've not heard any to confirm though. The Wharfedale Linton Heritage including stands looks to be in your budget and despite the 1960s styling, appears to be a bang up to date in sound quality and overall performance.
Of our active favourites here, might Neumann do better here as I gather the balance may not be as as 'bright' in a given room as Genelecs are reported to be (I'd suggest it's dispersion rather than on-axis response)? I wish I could get to hear some to tell you definitively as on-axis response doesn't tell the entire story once these speakers are used in a typical *domestic* room with heaven knows what acoustic. DSP can help here though to tame excesses and maybe gently eq the balance to suit and of course most actives worth their salt have some bass and hf correction switches on their backs to help..
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