If the known people possibilities fall through, can you afford to offer a good sized deposit that has specific details on how you get it back?
My husband is a retired Marine. So we used to move a lot. We always rented, and always had 2 large dogs that were over 60lbs, plus a cat who eventually was older than dirt while renting still. We never lied about ages, though I can say I did call my cat 'adult, not 'almost 20 years old' lol, as she was housebroken until literally the day she was put down at 23).
We always welcomed them to speak to our previous landlords, made it a point to mention that I work from home (I know not an option for all, but the time home with the animals is ideal for behavior issue prevention), and we offered larger deposits as well. I don't really agree with extra money per month, as unless it is in the 10$/month range, it is a massive ripoff if you are a good, quality owner. i.e. are you also willing to fix any issues yourself?

So our last rental, we paid a $400 deposit per animal, and 1st and last months' rent, all up front. We initially outlayed nearly $5000 to our landlords. That makes them feel much more secure on possible issues. The only stipulations we ever had regarding money automatically taken from the deposits was to pay for carpet cleaning, and that usually didn't even come from animal issues, but was even from the general deposit/1st/last month, as it is common to do it between tenants.
The last house did try to make us pay for a flea treatment for the yard and house when we moved out, which was not in our contract. We had their flea person come out and put in writing that we had no fleas and that if there was an issue, to put the blame on nature- squirrels, etc, or a neighbor' dog, as we had very clean healthy animals. (This was in SC where fleas are a major issue, so we had them on monthly preventative treatments, so no way any fleas could be from us.)
Anyhoo, I occasionally skulk around this forum, and thought those little tidbits might be useful! Good luck! And beautiful dog you have!