Yeah, it's starting to sound like maybe it's timing-chain related. If it's not flooded bad, then it's timing related. You have gas in the engine, and you have spark, so what's left is timing in these circumstances.
The distributor is driven by the camshaft. The camshaft is driven by the crank via a chain (i.e., the timing chain). The crank gear is all metal and pretty durable. The chain stretches over time, but overall it's pretty durable also. The "weak link" in the design is the cam gear. Stock GM cam gears have nylon teeth on them -- that's to make the engine run quieter. Those are only good for about 100,000 miles. With age, mileage, and heat from the engine the factory nylon teeth begin cracking and some can even fall off. As it wears, the timing chain gets looser and looser, and finally the timing chain can slip a few teeth. When that happens all the King's horses and all the King's men can't get the engine started again. Why? Because the timing of the valves opening and closing and the distributor firing is all out of kilter. That stuff all has to happen in a sequence that's dictated by the crank position, and if the timing chain slips it's all screwed up.
It doesn't take much to make that chain slip, either. It can happen just starting the car up. I've had it happen to me just setting at a stoplight, not touching the gas.
If that's the case, then what you need to do is to replace the timing chain. You get a new cam gear, a new timing chain, and a new crank gear -- replace them all as a set. You follow the procedure in the service manual and go from there.
It's not hard to do at all, and it's not very expensive. If your engine has 178K on it and it's either never been opened before then it needs replacement. Even if it was replaced once about 1/2 way through that interval, it's time anyway.
I'd start looking in that direction rather than fooling around with the carb, since the carb is new. Just satisfy yourself that you've done all you can do with the timing/distributor and make sure it's not just flooded badly first.