Hi and welcome!
This is a bit of a tricky one here. If it had a neck humbucker I would deem it easier to find something that can cover the range, but going with what there is my thought would be:
Bridge: Nailbomb. This does the heavy tones ace style. The most cited pickup for the bands you mention I think. Has the agressive grind and all that stuff. Normally I might say ceramic for these bands, but in light of the other pickups you might be better off with the alnico version. It is still plenty tight and has more of that organic roar to play nice with the rest. Roll down the volume and it is said to go well for rock too. Split it on top of that for even more play with the middle and such.
Middle: Here I would go Irish Tour. It is the quintessential single coil taken up a bit, without loosing that classic something. It is just a bit more powerful, fatter, slightly more rounded high end, more mids, and with a good pinch of a magic rock dust added. Plays well with humbuckers and does wonderful cleans. Just a tad warmer and more than a fully traditionall single coil. And when you add gain they react amazingly. Perfect for what you want I recon.
Neck: I think here it will come down to either the Flat 50 or 52. I am not familiar enough with them to be sure which tbh. However both are said to be extremly lovely, one being a bit more stratty than the other. In terms of power they again like the IT are a not low output but not screaming either. Just that thing you want for great full mojo cleans and then the ability to go up in gain. Also able to not fall off from the bridge entirely.
That is my take at least. Hope this helps. Lets see what the others think. =)