I see exactly the same thing when soft-proofing from the Moab profiles for my Epson 4000. Perhaps one of the colour experts will read this and chime in with an explanation.
Understanding full well your not wanting to waste paper, nevertheless, I suggest you sacrifice one or two sheets for testing so that the others may live. Print small sections and/or small versions of whole images, such that you run multiple tests on the same sheet, or cut a sheet into 4x6s. Concentrate on what are likely to be problem areas: black clipping, shadow colours, near-whites, and highly saturated colours.
If my experience with the 4000 holds for your 2400, you'll find Entrada Bright White is weaker in black and possibly bright red compared to Epson's Archival (AKA Enhanced) Matte. (Perversely, Entrada Natural White has better blacks than Entrada Bright White.) I suggest you abandon any attempt to work with the Moab profiles and try the Archival Matte profile - it works smashingly for me, both for print accuracy and soft-proofing accuracy. If that fails, you may have no recourse but to take an expensive gamble with custom profiles.