For reds, you need the double recessive non-extension ee gene, as well as a strong dose of rufus modifiers, which turn the golden tan shades into reds. So lets start with the essential non-extension gene. There are two main versions of the pigment melanin that tints hair and skin. Eumelanin is dark, can be black, reduced in intensity to blue, or phased down to browns such as chocolate or lilac; pheomelanin is light, the yellowish shades of fawns, torts and reds. Non-extension eliminates the dark color on the body hairs (not the points in the case of torts). In a fawn agouti, the dark color is eliminated entirely (except maybe for a few stray dark hairs called smut), and you have a yellow-tan rabbit without the rufus (called fawn or orange depending on the breed), up to orange to dark red rabbits (called reds). If you add in recessive color dilution, the color becomes more pastel, beige.
In non-agouti rabbits, you get tortoiseshell with the ee non-extension gene. The body color is still the same beige, yellow to red fawn shades, but the face color reflects the black/blue/chocolate/lilac genetics of the black/chocolate 'B' gene and the 'D' color dilution gene. Your doe can only pass along a recessive fawn gene, because that is all she has to offer. BUT, your other bucks are unknowns in the 'E' gene department. You need two fawn genes to get red.
Red New Zealand rabbits are fawn agouti with a lot of rufus modifiers. So your doe will be A- for agouti, and ee for non-extension, with +++++? we'll say for rufus. Two of your bucks are REW, which is simply any possible genetic with the albino recessive that shuts off the melanin factories, so no pigment is produced. We have no further information on them based on their color. Light gray is a chinchilla Flemish. The chin gene removes all fawn shades from the hairshaft, so that would be a terrible choice. Gold-tipped steel tells us two things. One, the rabbit has a dominant color 'C' gene, not chinchilla, because steel + chinchilla = silver tipped steel (remember, chin removes the the gold shades, leaving only pearly white, the 'silver' in the name.) The other thing is that there are five possible choices on the 'E' gene, and steel is the second most dominant, even more than the standard agouti and self colors like castor, black, chocolate, etc. It is coded with a capital E for being dominant, and a small super or subscript s for steel. What we don't know is what the second 'E' series allele is that goes with his E(s). BEW would definitely not help this at all, as the BEW albino gene also removes all color, and when it is combined with a more dominant non-BEW gene, often leaves white mismarks on face and toes.
So, the big question is, what do you know about the parentage of your bucks? Do any of them have tort or fawn/orange/red parents? An albino can throw red, but only if it genetically carries red, it's only an albino because recessive cc turns off the pigment cells.
Rufus modifiers are cumulative, think of them as plus and minus signs--the more plus signs, the darker the red. If you imagine a dark red as having five or six plus signs out of six, and a pale tort as having only one or two plus signs (or maybe none), the kits will have a good chance of being anywhere in the middle, not a super dark red. You'll want to keep the darkest kits of each generation, to work your way to consistent reds.
Wideband chestnuts usually come out of a red program; I have found that they can be useful to breed back into a red breeding program, because not only do they carry that wideband gene or genes but they also carry rufus modifiers from their red progenitors.
