The GR02 sounds like a good fit. The MH1C is pretty good for the price as well, and compete with the rest of the stuff common in your budget as well. I only say this because they're the first things that come to mind when "warm" and "fun" are brought up.
I thought my SRH840 had a great tonality for jazz and classical. I also think Doc mentioned the DT1350 being sold used in the for sale forums at that price, and I usually hear good things about them for classical.
Not really much in the way in terms of portable stuff (excluding IEMs, which you specifically ruled out) that could be considered as a complete upgrade to the HD25-1 II. Sidegrades are galore, like the DT1350, K550 (okay, not exactly the most portable, but that what they're targeted as), SRH940, etc. If you're looking for a full-sized as an upgrade, though, the HE-400s are punchy without being excessive, and one of the best choices for a mid-fi can at the moment. Also relatively easier to power, though they'd still like a bit more to sound their best. I'm running them off some speaker taps with the mini-X a-100, which is complete and total overkill, not only for these cans, but for anything other than HE-6/K1000s really. But they do sound great on them. A E10/17 should drive them well enough. Grab the HiFiMANs B-stock at Headroom, plus the E10s at $60, and it barely goes over $400. Other contenders would be the D2000 or the HD650, but the former might not suit acoustic well enough, and the HD650 need considerably more investment for a entire rig (Lowest for these would be 399, add an amp like the Asgard or O2, and yeah, pretty over budget)