[Dyl]

Matthew,
I use EZDrummer so I might be able to help but I'm not sure I fully understand your question.
It sounds like you need to overdub hihats onto your existing kick and snare midi and then have that routed to a separate track for mixing separately?
Once you've set up your EZDrummer tracks you can create a track(s) template that will save all your settings from Reaper's Track menu.

Your image looks like you've set up Reaper to have 16 channels of MIDI.
Have you routed EZDrummer to multichannel output? Looks like it because you've named the tracks to match the channel numbers EZDrummer uses.
Have you set the EZDrummer track (the track the EZDrummer VST is sat on) in Reaper to allow midi overdub? In your image it's the "in" button just below the lit record arm symbol. Look at the input settings for midi record, choose overdub.
With these settings you should be able to record your new drum parts via a midi controller just like an overdub. The channel routing should have the hats go to it's own track that you've got named as hihats. You can then add effects there.
I'd say from experience that it's better to render your midi to audio and then add effects but that's a different topic.
Anyway, hope this helps. Shout up if I've missed the point and I will try to help if I can.


EDIT:
just looking at your question again, I can see in the image you've got two takes. If you are using overdub it just adds the midi to the original midi, no second take, so that looks like you need the midi overdub record setting on the input of the EZDrummer track. You can then mix on separate tracks like you wanted. The toms, I forgot about. Do you mean each individual tom? I've not found a way to do that in EZDrummer. EZDrummer has them routed to the one channel so you are limited there. Superior Drummer separates all the toms out and is worth the upgrade if you can afford it. Massive step up from EZDrummer but can be a bit tricky to get used to after EZDrummer.
Maybe there is an advanced way to separate midi notes in Reaper's piano roll (so each individual tom F2, G2, A2 etc) go to a separate tracks in the TCP. Never tried that but I will have a look.