You're doing awesome - you're saving almost 50 percent!!!
$1500/month for a 2 BR in LA is really cheap. My guess is you're in a neighborhood that also has homes for under $500k, so it could be very doable to buy a home if you like the area. LA has this reputation for being outrageous for buying, but it's a totally different situation buying in Santa Monica or Bel Air than it is somewhere like the San Fernando or San Gabriel valleys. Last time I checked, home prices per square foot were about the same where I live (a decent part of SFV) as Seattle or parts of Denver. It's the nature of metropolitan city living.
Mozar's calculation (income x3) was using your current income and not accounting for your wife's potential raise. That alone would put you at around $300k for a home, and that's just today, and not your income in 3 years. Another calculation is the percentage of your income - lenders generally want mortgage to be less than 30% of your income, but in LA you can find lenders who approve for closer to 40% (whether or not you want to do that is another discussion)
Using my own home as a comparison... It's 1700 sq feet, was move in ready and is in a decent neighborhood (mile up is a bit rough, mile down is mansions - typical of LA). It was $400k, 20% down (80k we saved over 3 years), 4.8% interest, and the monthly payment was $1750. Earthquake insurance and homeowners was another $150/month and property tax about $350/month. Our income at the time was probably closer to 100k combined, and we were 32 and 29. That was coming from a rent payment of $1500, but because we had been saving at a very high rate (probably 40% or more) it wasn't a huge adjustment - money just shifted to house vs savings. I refinanced a couple years ago at 3.8% for a monthly mortgage of $1400.
I am 110% glad we bought. It's not just about an investment, but also a life choice. For us, it wasn't about online calculators or what the bank said we could afford, but rather if we could pay our expenses on one salary. PMI would have been $200/month down the drain, so that dictated our maximum purchase price. We also cut costs by having a friend live in our spare bedroom for a couple years, and put his rent towards extra principal payments. A lot of homes have converted garages, which works great for a renter if the garage is separate from the house (not always legal, but it's common and cuts costs)
Additionally, if you are still doing the side gig, you can itemize a number of your house expenses on your taxes (square footage of your work room, corresponding percentage of your utilities and repairs). Are you currently itemizing expenses for your business on your taxes?