Yes, exactly as you said, we are trying to co-cluster our sc and bulk data, with the idea that distinct clones agree with distinct single cell subtypes.
By 'seeing where the 3 cancer clones fall on this UMAP plot?', I mean adding each clone as a separate data point to the UMAP plot, and seeing what cluster each data point is in.
Yeah, I think you're right, it might not be possible to integrate the sc and bulk data. We'll probably have to do you DE approach or the ssGSEA idea listed above
Instead of normalization, you can also try to use custom distances like cosine-distance, which implicitly normalizes data.