I mean listen to the sound of, say, RAMI's bass drum. Scroll through all your bass drum samples, and find the one that most resembles his tone, tuning, attack and decay. Then use the EQ on your board to fine-tune the frequency representations of the audio sample to get it closer. [I find, generally, that real drums have more sub 300Hz and more 800 to 4000Hz than my synth's samples...giving more 'tub' and 'attack'. I use a parametric EQ . And I get as close as I can. Then I record that sound to an audio track, using the bass drum midi data. [if your midi drum data is all on one track, make several clones, and delete everything in the cloned track except the one piece you want to record. Split the data if you have to...if the sound you find is part of a 'kit' in the synth. [might be another way, but that's what I do]
I do the same for every part of the kit. And when I'm done, I have a much nearer representation of a real drum kit.
Then I mix and pan the new 'kit' in audio to itself on the platform, and then mix the entire 'kit' into the tune, continuing to reference RAMI's tune.
I guess you could also assemble everything as a custom synth kit, and actually use the synths parameters to tweak the sounds. That would take me a long, long time....I'd have to read the manual.
I've done this three times. And it's a good ear trainer, not being a drummer n' all. Focuses attention on a personal weakness, for me. I did it last week, using the same RAMI tune as a model, but the end result didn't work for the non-rock tune and mix I tried it on. But your's is a lot closer to RAMI's thing, and it might work well.