Hi Mike,
The monitor is a calibrated EIZO CS2730, so I suppose the issue is not here.
I'll follow you advice and start from scratch. I'll buy some epson sheets and try them out with the Epson ICC profiles.
The custom profile we use now was made by the company who sold us the printer. I sent them one of those color checkers printed with our printer on permajet oyster paper and they sent us an ICC profile back. Unfortunatly, our prints came out too dark. To solve that issue, I fiddled around in the printer driver and found out that by setting the gamma to 1.8 our prints came out perfect. So yes, as you mention it's double profiling to correct what I suppose is an ICC profile that is not correctly made. It always bugged me that I had to set that gamma setting, but since we didn't have the need to change papers and the results were very satisfying I just left it like that.
The issue somehow resurfaces now, because I'm experimenting with other papers types. I bought some Permajet Matt Plus paper, that I use with the ICC profile from their website but the results aren't satisfying.
Their profile only mentions "EAM" which is Epson Archival Matte (which
according to some is equal to "Ultra Premium Paper Presentation Matte" and "Enhanced Matte", the driver doesn't list Epson Archival Matte in the media types). There's many information on their website, so perhaps I missed something regarding the driver settings.
I'll do some more test and eventually get back with some results.
Cheers,
Dimitri