Similar animated LED signs are turning up in more and more places of retail. See if you can find out where they got their signs made.
Then visit the signmaker and pick up any information, price lists, etc. Do not let on you want to compete.
Or can you look through electronic supply catalogs and find similar signs? Or smaller ones surplus or used. Their prices might be guidelines for your bid.
Can you locate a manufacturer who will supply a ready-made LED board with the spacing and dimensions you want? Also grid hookup wiring. Power supply. Driving and/or multiplexing devices, if that comes with the technology. Because ready-made might cost less than gathering all the loose parts and assembling it yourself.
Or, is an elliptical LED board a specialty item which costs more than a rectangular board? If so (or if you can't obtain an elliptical), then can you start with a rectangular board and mask over it to make an elliptical opening? This method might also be needed if the software/ hardware cannot create an elliptical image.