Thanks for all the great inputs so far! Yeah I'm definitely more inclined to feel like the natural fix lies in bringing more low / low-mid to the party. I tinkered a little with the specific frequencies mentioned and got closer to something I like, but there's still a blary quality persisting in the product.
You're right to assume that I was pretty far back-- the event had set up tons of delay towers all the way down the National Mall, but I don't believe they included any subs, so my low-end was probably about 7 city blocks away (which also makes sense for why it tends to sound out of sync with the music).
Am I wrong to feel that there is a way of EQ'ing this into something I could be happy with? Is it possible to "cure" a weird sounding recording?
Thanks for all the help so far!
Well the blare-y thing you can probably address by not going too heavy on the upper-mids and perhaps dropping the upper-mids and highs to get a more natural overall curve.
The positional background helps. I'm quite familiar with the Mall but would only go there to record Folk Life, or when I was younger and the music was good Inaugural events, where you're dealing with a large tent at most.
If the delay towers didn't have all the sound and you've got internal phase contradictions mixed together (the out of sync thing) that may not really be fixable but would explain "blurriness". perhaps that is behind the other suggestion to just cut the lows but I don't think that works with this sort of music.
Phase left-right can be fixed. Phase of an entire part of the spectrum vs. other parts of the spectrum I'm not so sure unless they are discrete. If that internal phase contradiction is really your issue and there is some sort of clear division in the ranges you could essentially go multitrack and double both channels (make it two sets of the same content in a multitrack editor). Then kill all the highs above your break point threshold on one set and all the lows below the breakpoint threshold on the other. You would probably have to experiment to see where the right breakpoint is. Then time align those two components with each other as if they were out of phase channels and mix back together. That might get you somewhere (essentially moving the bass frequencies only that were coming from way far away
back forward on the timeline to get aligned with the rest of the sound that you were getting a closer read on). You can eq those components independently to get a better sound out of them before combining them and in combining them can vary the output levels to play with the balance of them. Maybe try that for a few minutes?
I would agree that often what people think is an eq or frequency problem can be a phase issue (and phase can take different forms). You did at least clearly get to what your problem was with a little back and forth here. The problem is whether it is fixable, since differing timelines were all mashed together where you were (and then as you recorded it).