Hey! Thanks a bunch for purchasing the tileset, please go ahead and share it with your team, I'd really like to see the results when you have made something with it!
I did some "colorizing" with a previous tileset, by doing basically what you described- I opened the set in Aseprite (which I fully recommend, it's awesome), swapped the colors and just pasted the recolored version into a large "atlas". Just find a palette that works for you, and you can get it done in a relatively short time.
Maybe I should make some color variations and include them with the tileset, too?