Make an action in Photoshop to convert to grayscale and flatten, then run a batch on the images and use the grayscale versions. Non-transparent grayscale images can be colored with whatever you like in ID by either draggng a swatch onto them or using the Direct Select tool to selec the image then choose a fill color.
Unfortunately the image is being supplied into a web-based Indesign document template so we can't use the Photoshop route, that's why I'm searching for a Transparency route within Indesign.
Not going to happen.
You'll either need to make clear to users of the template that they need to supply the correct form of art or do the conversion yourself. I expect it could be scripted to find these images open them in photoshop, run an action, and return them to ID as grayscale. It probably could be set to run on file open.