I think .icc and .icm are interchangeable, certainly Windows can work with either. The profiles I generate are .icc and work across platforms. Although from what I understand some older versions of MacOS need profiles to 'be converted' from the current ICC standard.
I think the issues you are describing may relate to the shadow performance of the papers. Matte paper (no matter the printer) is capable of less shadow detail than gloss or lustre paper. Some printers are linearised better (Epson 4800, 7800 etc) and are there better at extracting what shadow detail there is.
Also you need to consider the optimum inking levels of the papers. Some non-epson papers definitely benefit from less ink. The excess of inks sometimes causes poorer shadow detail and sometimes pooling.
The inking or color density levels can be optimised prior to profiling the paper by printing out wedges at different paper settings and ink densities.
It is my understanding that the media black point for profiles of any paper are relative. The settings relate to how the colour rendering engine translates from the working colour space to the paper gamut space.
If you would like me to look at the two profiles you are talking about then feel free to email them to me.