I think a fundamental part of your success is going to be getting your wife on board. That's clearly not going to be easy; I think you have an uphill (though not impossible) battle. I'm rooting for you.
Some easier things to address/resources:
Another resource is budgetbytes.com for good cheap food (including many vegetarian meals). Generally, beans are cheap, and you can cook them in very large batches to keep in the fridge. Eggs are cheap and quick and easy. A bowl of steaming grits with beans and a poached egg on top, with some greens or grilled peppers n onions and a dash of hot sauce? Delicious and fulfilling vegetarian food on the cheap, and the only "expensive" thing is the peppers. A bowl of shredded cabbage, carrots, black beans, tomatoes, bell pepper, topped with a dash of homemade dressing and a splash of shredded cheese? Delicious, filling, low carb, high fiber vegetarian food, and again pretty cheap -- tomatoes, bell peppers, and shredded cheese are your most expensive items.
I added up your monthly income and your monthly expenses, and though I may have missed something in doing my calculations, I'm finding 732 dollars that aren't accounted for -- 732 dollars that are getting spent somehow, somewhere, and not going into your savings accounts. Where's that money going? That's more than you net in your side gig every month, mysteriously disappearing.
How far do you live from work? $120 is more than I spent on gas every month when I was driving 60 miles round trip to work every day, and I live in California, land of high gas prices and incredibly dumb, gas-guzzling traffic congestion. Could one of you walk or bike to work? It's cheaper, it's healthier, and it's frankly way more pleasant than driving. And if you're that far from work, why not move? It looks like you have close to median rent for your area; can you not get median rent near at least one of your workplaces? Maybe even below-median rent?
Also, is your savings automated? If not, I'd suggest doing that. Pay yourself first and make it easy and effortless. If you don't miss the $25, try upping it -- $50, $100, whatever. Keep adjusting as time goes on.