The EEM paper that you insist on using is quite well known to loose its whiteness in quite a short time, and is generally accepted that it is not of archival quality (although much better than other non-archival papers).
Relaxing your criteria for brighness, will help you solve the problem with EEM overinking as well. EEM i found to be good for proofing, too thin for much else.
I don't know what you mean by "quite a short time" and then there is a question of the storage conditions. It is necessary to be more precise in discussing these things otherwise people can misunderstand.
EEM like other matte papers is relatively short on D-Max and can block detail in deep three-quarter-tones, but it is an eminently useful paper depending on the purpose. I use it extensively, but I don't sell my work. If I sold my work I would prefer to use a heavier stock.
Getting back to its properties, if I post these prints on the fridge door, within a year they lose a bit of their original whiteness. When they are kept in dark storage or in bound books as I described in my recent article on this website, the difference in whiteness is hardly noticeable after two years and somewhat noticeable after five years. I am printing as I write and I just made the comparison of a print fresh out my 4800 with stuff on my bookshelf this minute, under D-50 illumination.
As for over-inking, this depends on printer settings and adjustments, not on the paper. I see no evidence of over-inking from my 4800; I do not consider the deep quarter-tone issue a matter of over-inking, based on similar results I've seen from other printers on the same files - be it with the Epson driver or ImagePrint - unless all of them over-ink regardless of what one does - perhaps not likely.