Your budget is completely reasonable, and you probably can't milk much more out of it.
That said, you guys are in a great position.
To free up more money, the only thing you can really do is to wait. Let that $500/mo of emergency fund build up to whatever your target emergency fund is, and stop contributing. Build up your home down payment of $1000/mo to where you want it to be, and stop contributing. Build up your car savings of $300/mo to where you want it to be, and stop contributing. All of a sudden you have $1800/mo extra towards investments, or $21,600 extra. This puts you above your $40k goal, without even cutting back on your vacation savings, which you could do as well.
To top it off, you guys will likely be increasing in income in the next few years, and I bet you can FIRE in less than 10 comfortably.
You've already won, you just have to play out the steps. Good job :)