I finally got the impulse line off. Removing the handle allowed better access to the left side gap and I was able to get a pair of hemostats in there. Still couldn't see much, but it wasn't too hard to feel what to do. The impulse line was in good shape - no cracks/holes. I put it back together and scratched my head some more. I checked the impulse by hooking my mityvac to the carb connection on the impulse line and cranked it. Plus/minus 4 or 5 psi/inHg indicated sufficient impulse, since I saw that fuel was being pulled through the fuel line with next to no vacuum.
So, must be the carb. Given the new kit and otherwise new looking carburator, I couldn't quite pull the plug on it. I pulled it off again, to triple check everything. One thing I learned was that there was a gauge for setting the metering level. I had seen in discussions that the metering level was either supposed to be level with the face of the carb housing it mounted into, or set according to the gauge. I didn't have a gauge, so tried to set it as close as possible to gauge depth using other tools. I put it back together, and it still wouldn't fire.
I knew from before it had spark and would fire with fuel injected directly, so I got my syringe and verified that again. This time, I put a bit more fuel into the carb, and it would sputter for a second or two. In my frustration, I pulled the throttle and it tried to run, but would choke down. A few more attempts and I got it to run as long as I held the throttle. I had previously set the high and low screws to the factory setting of one turn out each. At this point, I adjusted the low screw to 1.5 turns out and off she went, running without me having to hold the throttle. Minor adjustments from there on the low and idle screws and she runs and cranks very well. A day later it started on the 1st pull.
I'm a little baffled still that the factory settings on the carb wouldn't even give me a sputter, but I know a lot more than before, and I have a good running saw.
Thanks again everyone for the guidance.