Toro Single Stage SnowBlower - Hard to Pull Start

I'm not familiar with that machine however if the engine runs fine once started, there's nothing wrong with the flywheel / keyway  
 
 The gear on the outside of the flywheel for the electric start has to be good or it wouldn't spin it over. 
 
If you can post up what the engine is specifically, it can be checked (parts diagram) for a compression release located on the cam shaft.
 
Should that be the issue, pulling at least the side cover(RS) would be required to access the camshaft..

This is a two-stroke engine.

Interesting....  
 
The compression release, looking at a parts pic, seems to be reed style valve:

 
The only thing I can think of is to check for any play in crankshaft, on both ends. Pull / push in all directions checking for any play.
A very long shot but possibly the flywheel is indeed hitting the coil if the engine has worn bearings..
 
Good thing is the electric start works...  I would make sure any part you may want to pull (gasket, etc) is still available. 
 
Please post back if you find the issue, good luck.
 
 

I'm not sure exactly how a "reed valve style" compression release works. 
 
The parts diagram indicates it's pretty easy to replace and there really isn't any other moving parts to fail/be the issue...
 
It certainly can't hurt to replace it and can only help... 
 
Please post back how it goes, if it goes, etc..

I had a non start Poulan Pro blower (2 stroke) that indeed had the ring carboned up. 
Once cleaned, it starts / runs fine:
 

 
Recently, I had a weed eater that didn't want to start.  I set the engine at TDC and put Seafoam in the cylinder and let sit for a day.  It cranked up first pull the next day and still runs fine...
 
If you can look into the exhaust port and check the piston for any scoring would be helpful.  Checking compression, at least 100PSI would also help with diagnosis.   A peek down the cylinder with a bore scope/camera would also be helpful if possible...
 
Pulling the cylinder and cleaning the ring(s) isn't that hard.  Just make sure you have gaskets etc.  As for torque, good and snug with RED loctite has worked fine for me...  
 
I would check the above first (and Seafoam), before pulling the top end apart.  As it is an older engine, a new piston ring couldn't hurt..

Excellent!  Glad it worked out for ya...
 
For long time storage, I'd run the engine bone dry of fuel. (Generators for down here in Fl.) 
If a steel fuel tank, some pre-mix to keep rust from getting inside the tank. Dump before using.
I also put either a couple teaspoons of Seafoam in the top end (inside spark plug hole) and crank
over slowly to distribute and keep the internals moist with oil...
Leave the engine at TDC to keep moisture from getting in the cylinder.
If a butterfly choke, leave it closed as well (prevent critters from entering) 
 
Yamaha's Ring Free is a fuel additive I use in EVERY MACHINE I own or repair...  
It helps with carbon build up and cleaning the fuel system...