You answered your own question kinda when you told us you already know what bid your up against.
If you don't want to be greedy which isn't what pricing appropriately is but ok, Bid them at $24, Your saving them $20 overall compared to the other bid. Get as much as you can, Without going too high and since you already know what your up against, This should be easy.
".080 or .808 Whatever. They are just parking signs. I am going to use
the aluminum we have, I am sure it will be fine."
Heck, Use coroplast then. I'm sure it will look real professional since they are just parking signs.