You'd need a 4-pole double-throw on/on/on switch if you wanted a single master series/parallel/split switch that did the same thing for both pickups. You can get mini-toggle switches like this, but with four poles,it will be quite wide, so unlikely to fit in the same position as the pickup selector switch unless you increased the size of the rout.

You do have room to do this under the big scratchplate, and it doesn't have to be neat as it will all be hidden!

Two two-pole/double-throw on/on/on mini-toggles might be a better option if fitting them in the wiring channel, but fitting them near the volume and tone controls would be much neater from a wiring routing view.

The pickup leads will go to the toggle switch, then to the volume/tone controls, then to the pickup selector switch and then back down to the output jack. Having the toggle switches in that upper wiring channel will involve a lot of wire crossing. If you have space to fit them by the volume/tone controls, then the wiring becomes a lot easier and less tangled, though there's not a lot of space in that area to fit them so they aren't in the way, at least not without routing out some extra room or fitting them in the lower wiring channel and having them operate at a slight angle.

Push/pull switches are good for doing coil splitting but you only get two positions, so you can't do series/parallel/split on them. I prefer push/push switches as they are far easier to operate, but they only seem to come in 500k versions (or at least that's all my normal guitar electronics suppliers seem to stock). 500k is fine for humbuckers, so if you can live with series and split options, you can see if you can find some.

Always check the depth of your control cavity before getting push/pull or push/push pot switches. You want short-shaft pots as they are fitted direct to a scratchplate, but if you can only find medium shaft pots, they will have to be spaced off the rear of the scratchplate with a nut and washer, increasing their effective depth. Either that, or else the knobs sit very high from the scratchplate, which isn't a good look.