Not sure if this will help ... but I am thinking that the canister-bill dispenser in our ATM could be very similar to your dispenser.
What we do is use our better $5s from our bays but also as in every other one we put a brand new that we get from our bank. Caveat because brand new bills have a tendency to stick together if we ever use 2 brand new next to each other we first crumple up one of them so we don't inadvertently shortchange ourselves.
I have heard that there are bill dispensers that actually have internal recyclers within them but I tend to be a bit skeptical on how well they work ... but I don't honestly have any 1st hand experience with those specific changemakers.
The nice part about dispensing our $5s from our ATM is that the direction of profit is more in our favor than no surcharge or going the "at the mercy of merchant fees route". Customers are not as stupid as we sometimes think when it comes to seeing an ATM equipped self serve with a better value than a bit too much cashless unnecessarily higher priced self service car wash IMHO. Admittedly ... non self serve car auto washes tend to have other considerations though ... before one of the jackasses on the forum twist my words ... like main stream media has proven themselves to do!!!