FHA loans have a cieling, not sure but it was 417k, it’s usually at or below conforming.
Hey, here’s a novel idea, buy a house that you can afford on the 125k and then if you keep the second income, live like a rockstar or pay off the house in just a few years, underextending is the new black. Keep your credit rating, sleep well, eat well and drink well. I paid a little over two years pay for my place and I can attest that the peace of mind of underextending is fabulous. It will give you room to play the stock market, contemplate rentals or do whatever. Sinking it all in your primary is so 2006.