I think that if only emerald cuts are allowed, and emerald and princess cuts are not allowed, them emerald cuts are not allowed which I think leaves only emerald shape, but uncut as the only possible option. Can you please clarify the criteria? Would a todd reed eternity of uncut diamond cubes meet the criteria?
I realize this is not quite what you are looking for, and it is out of budget, but thought I should throw it out there.
a diamond and sapphire eternity ring that turns into a ruby and diamond eternity ring!
If you're open to the idea of rectangular baguettes in lieu of an emerald cut's step-cut faceting, Caysie vab Bebber (CVBInspiredDesign on etsy) offers a band with French cut, unheated Yogo sapphire baguettes that would be comfortably within your budget. This photo depicts the band with purple Yogo sapphires, but it's also available with the more usual, blue Yogos, and with or without the millegraine edging.
I would suggest that you ask to see pics of the particular Yogos she would use in the band made for you; the blue Yogos in the diamond & Yogo eternity band shown in another of her listings aren't the richer blue I expect of Yogos -- altho' that may be due to the photography and/or my computer monitor. And you may have to pay more for a ring with better Yogos, like those in this pin I've long lusted after: http://www.ebay.com/itm/Vintage-Yog...-Natural-Pearl-14k-Platinum-Pin-/400712551643