Honestly, I think a strat would fit the bill for what you described especially one fitted with a humbucker at the bridge. Otherwise, many people consider semi-hollowbody guitars to be among the most versatile guitars. Though if you mostly play metal, it may not be the best choice. (I personally use mostly a single semi-hollow for a wide variety of styles, but I don't really play much metal or high-gain music these days).
In general I'd aim for a bridge humbucker for the metal stuff. A variety of pickups in the neck position could work for other styles or leads. The output/volume of the pickups is also a factor. For metal/modern tones you'd usually want a hot pickup but for cleaner and vintage tones you might want something a with a bit less output. So maybe a hot humbucker at the bridge and something with a little less output in the neck position?
Another thing I'd consider is the position of the neck pickup. Many shredder-style guitars have 24 frets which requires the neck pickup to be slightly closer to the bridge than on a 21/22 fret guitar. This is actually nice for some kinds of shred leads because it will make the neck tone a bit brighter than it would be which usually helps it cut through the mix more.
But for an optimum thick, bluesy, neck tone, you want the pickup to be positioned about where that 24th fret would be and it can't be if the neck extends that far. So consider what type of neck tone you need and whether you'll actually use those extra few frets.
As far as scale length, longer scale lengths (ex. strat/tele) will have more tension using the same string gauge—affecting the feel for better or worse depending on preference—and will generally produce a clearer and more focused tone. Shorter scale lengths (ex. les paul) will have less string tension and sound a bit warmer. There's no best; they're just different.
Compromise or Compliment?
All that said, it's pretty hard to get a single guitar to cover a wide variety of styles well. You'll always be compromising somewhere. So I'd consider splitting your budget to get two cheaper but vastly different guitars to cover more ground. Or make your new guitar one that compliments the ones you already have rather than looking for one that does everything.