I have a labrador and it's almost impossible for me to find an apartment either, I even upped my price to $5k a month and I still can't find anything that isn't awful (and that's ignoring the price).
The first problem is most places are not pet friendly at all. Then when you find a place that does accept pets, they almost never accept large pets. And even the places that supposedly accept large pets are always going to choose the tenant that does not have a pet, even if you offer more money. In SF, where there are multiple bidders on everything, it's almost impossible to find a place if you have a large dog. As someone who's lived with large dogs his whole life I have always had this problem, but not nearly as bad as it currently is in SF.
I've been so frustrated with this lately I actually tried to think of a way to solve this problem from a business perspective, but haven't come up with anything much better than being a super niche insurance company which would have an incredibly hard time getting buy-in from landlords (who hold all the power already). There's no doubt in my mind pet owners, or would-be pet owners, would be willing to pay more for their loved ones - but how to create a market for that when the landlords hold all the cards is something I haven't figured out yet.
And "large" is a loose definition out here. There are some places with weight restrictions at 50 lbs, and I've started seeing more and more at 35 lbs or even 25 lbs!
I only had found two places that were okay with my dog back then.