First, I would talk to management and see if things can be arranged that BOTH agencies can work together. With soo many animal rescue groups out there, the more the merrier! Who knows, the two groups may be able to "share" their volunteers so you can fit into the new restrictions.
Here's my "constructive critiscism". Does it ONLY have to be one volunteer for the 4-8 and weekends? Can't different volunteers split up the times between everyone? Maybe one can work only 2 hours and another pick up the slack. That should still leave time for someone to have a "life".
I can understand the "no eating on the floor rule". It's extremely unprofessional. Most employees I know in "retail" aren't allowed to eat on the floor. (Petsmart is retail). Plus you have many people coming in and out with animals smelling the food. This can cause some serious issues with pets if they smell food.
I am not a big Petsmart fan myself. I've worked at Pet stores in the past. They usually come into business to close down the competition. Smaller pet stores can't compete as well.
There are other ways of getting your animals out there besides Pet smart or other stores like that. How about fleamarkets? Special events like charity walks or other charity events? News media or newspaper. Cable advertising is BIG here with one local rescue organization. (Although they are the worst rescue group ) The internet is a really growing oportunity. Find other avenues to get your message out. You may be surprised and successful at it! Why limit yourself to Petsmart?