Reminds me (painfully) of our start to 2013. Bought a new house, hitting our savings a bit to do so. Two weeks after moving in, had to replace the sewer line. Not nearly as pricey as yours (we're only 32' from the curb) but it killed most of our incidental move-in budget... furniture, minor repairs, etc. Then came baby (two weeks later.) Then came the unpaid furloughs from work (two months later--BOTH of us.) Then came the notice that our work's daycare was unexpectedly over capacity (military families get top priority and they bumped us down the list) so we've had to pay $600/month more for daycare than we originally budgeted.
We made some sacrifices, like having our second bedroom converted to a makeshift garage/storage area. (We were going to build a garage ASAP after moving in, but the sewer bill, furloughs, and daycare SNAFU ate up all that money.) We're doing the best we can to make the visible parts of the house look decent while trying to hide the squalor upstairs and pretend it doesn't bother us. Having a new baby in the house is stressful, time-consuming, and expensive, but he keeps us sane and brings us so much joy that at the end of the day I don't really care about all the other stuff. So far, we haven't had to borrow, although our savings can't really take any more big hits before that becomes necessary.
You are doing things right. Definitely leave no stone unturned in trying to defray some of the sewer line cost, but keep in mind that as long as you continue to practice fiscal responsibility, you will be better off than 99.9% of people that get dealt the same bad luck. Over the long haul, you will be better for it, and you now have even more incentive to value a good strong savings buffer.
We were SOL on getting any of our sewer replacement costs defrayed. It was a 60 year old terra-cotta pipe... they are expected to fail in that timeframe. The seller was a lawyer and while they likely knew something was up, they didn't have any work done on the house so it's unlikely there was a paper trail proving they were aware of the problem. Home inspections don't cover buried pipes. Insurance doesn't cover it in our case because it's just "worn out" and we all knew it would happen sooner or later. I was just hoping for at least a few months or years before we had to bite the bullet.
However, you said you have new construction... that's a whole different ballgame. I can't think of a good reason why any sewer line put in after the 1980s or so should have failed by now. Terra cotta hasn't been used in decades as far as I know. Cast iron should last 40-100 years. PVC is often quoted at 100 years+. I would think you are looking at improper installation, materials, or some external factor like nearby excavation or a geological event. In any of those cases I think you'd be able to go after the builder, or insurance.
The important thing is that you were able to get the shit flowing away from your house without going into the red. Now you can sort out the rest while being able to shower and take a dump whenever you feel the need. Don't discount that.