There's not a lot you can do to get around breed and size restrictions unless you're willing to lie and your potential landlords aren't doing much in the way of verification; in my experiences those aren't just guidelines, but are hard and fast rules that are often bound to a landlord's insurance. You can round your lab/pit mix down to a lab mix or shave off a few pounds when listing their weights, but you run the risk of landlords declining or evicting you if they get a look at the dogs and decide you weren't totally honest.
Good pet references can be very useful, though the potential landlords have to be willing to get far enough in the process to check in with them. However, mentioning early on that you can readily provide references, especially if those references include previous landlords, shows that you don't have anything to hide.
Some agencies/individuals will be more receptive if you can cite training or certifications your dogs have received. I've done a CGC prep course with my dogs, which was helpful not only in having landlords accept them, but in getting a lower pet deposit because they've shown they can be (fairly) well behaved and I am devoted to their training. Even if your dogs aren't perfect (mine aren't!), and even if you've only done basic training, mention it early because that will put you well above dog owners who don't mention it at all.
What I can't recommend is getting a doctor's note designating one or both of your dogs as support or therapy animals to get around pet restrictions. While this may help you get a place in the short term without as much hassle, in the long term, the surge of people using this loophole damages the reputations of actual working animals and responsible pet owners and encourages landlords to make pet ownership harder and more costly for potential tenants.