Just now getting to reply here, will do everyone at once.
The engine part # is 739-10676B.
I took the multimeter out after dinner this evening and checked the new coil. All is well with resistance so in a perfect world, it would produce a spark.
No points on this engine so we can rule that out.
Gunk in the carb or fuel lines could certainly be an issue. It did my best to clean the tank and replaced most of the fuel line, but it isn't perfect. I can see jets of gas coming out of the carb if I watch it while starting. I have no idea how much it is supposed to jet as I have no reference (again, this is my first engine project for the most part). All I know is that at least some gas is making it into the carb. I will say that when trying to start, the gas smell is pretty immense. It smells like the engine is being flooded, even after just the first attempt. Could be a leak somewhere in the line I suppose, but I see no obvious evidence.
I thought about spraying a little gas into the carb and trying to start it, but since the gas smell is so strong, I'm not sure that would help.
Spark plugs also smell of gas and I replaced them during this project...which means gas is making it where it needs to be.
Unfortunately I don't have a lot of tools at my disposal (compression tester, fuel pressure tester, spark tester, etc). I'm not opposed to picking up a few diagnostic items, but I could quickly go overboard trying to get this solved.
The manifold gaskets for the intake/exhaust were a little cracked up, but I put them back on as is. I plan to replace those if I get the thing running, but maybe that is contributing to the issue? I feel like it wouldn't have started last week if that were the problem (even partly).
Maybe I missed it above, but how can I test the ignition condenser?
Also, I thought about the safeties on it, particularly since the engine cut off when I engaged the sleeve hitch motor, but I was under the assumption that the engine wouldn't even try to turn over unless all of the safeties passed their check? If I do not depress the brake then the engine won't even turn over. Not sure if that remains true for all of the safeties?
FWIW, the engine isn't seized anymore, hasn't been for about a month. I quickly resolved that issue and it hasn't been a problem since (other than a weak battery not being able to turn it over properly).
BTW, I also checked resistance in the spark plug lines from the ignition coil to the plugs and I think those lines (both) are fine. They are a little cracked up on the outside, but if they test fine, I figure I'm not going to worry about it yet. Maybe I should go ahead and throw a couple of new spark plugs in there for the heck of it? I did it when I first started this project, but the plugs are definitely getting carboned up. Again, I have no reference as to how they should look at this point.