The old petcock  leaking into the cylinder and your continued cranking to try and start the bike many have scraped/washed all the oil from the rings and cylinder walls .Remove the sparkplug and add a tiny bit of oil to the cylinder it will help build added compression and ease starting ,as you have no oil to these parts until the motor runs.you haven't said you changed the oil and filter yet and that is very important. You should also check the air filter for gasoline and drain the air box using the tube that hangs down under the bike ,be sure to replace the plug in the drain  tube when finished.

Spin the starter with the plug out.
If it's not trying to start, check the plug.
Easy to get oil splash on it.
You don't have to put the tank on to just get it to fire.
Battery Voltage is crucial

Took out the air filter and shot some WD40 into the air box before reattempting.

Tried for about five minutes of off and on cranking and it’s definitely sputtering/firing weakly, but it won’t run on its own. I have to hold the starter on the entire time and it starts sputtering and smoking a little out of the air box, but it won’t catch and run on it’s own if that makes sense. Opening the throttle gently and just a little causes it to pick up a little more (slightly more RPM than whatever the starter spins it at).

first off,  don't keep holding the starter on ,if the bike doesn't start on the first few turns , it's not going to. running the starter to long will overheat and ruin it .after trying to start you need to let the starter rest/cool down for at least 10-20 min.
          If your going to spray anything in the air box WD-40 isn't it ! It could block your paper air filter or pass thru and make your slide stick. Where as starter fluid will help.
            The hose hanging down is the air box drain hose ,good news there is no oil in the air box, bad news ,this hose should be plugged, ( use a bolt and wire tie/hose clamp) any time the motor is running it will suck unfiltered air into the air box between the filter and carb sending grit into the motor.              

Brentr wrote on 04/15/18 at 09:02:45:

that's the battery vent, don't plug that.

Give it a whiff of ether.

If it won't cough, buck, and Try to start with ether
It's either flooded, wet plug, or no spark, barring a timing issue.

You can
Pull the plug and test for spark and all that proves is the ignition system and plug work.
Under compression the plug may not fire.
They are cheap
Get a new one
To test the ignition/battery
Get the plug in the wire
And put a plug in the head.
Make the battery pull the starter through compression and Then see if you have a spark.

I suspect you're trying to start it with a weak battery.
If it's a lead/acid
Pull it
Check the water level
Take it to be tested.

Regardless, have it tested.
Ether, in the intake, should have done Something..