I'll go ahead and answer my own questions, when possible in case others may later find this useful.

I slowly pulled the cord all the way out 'til I could see the pulley itself. The edges are ragged and uneven so I assume it is supposed to be one piece and now broken.

I found that the part is available but was told that due to its age, quite expensive and not worth replacing.
(If anyone has an old one kicking around that they'd like to sell for a reasonable price, please contact me. )

In the meantime, I'm going to try to remove it, clean and degrease it and glue it back together.

Not yet sure if this applies to mine or not, but to remove/replace the assembly, I found the following instructions: How to Install a Pull Cord for a Lawn-Boy Push Mower

One of the most common things to go wrong with any kind of mower, including Lawn Boy mowers, is that the pull cord simply won't "pull" anymore. Sometimes they break, and sometimes they just wear out. Knowing how to install a pull cord for a Lawn Boy Mower will save you from a wasted day and wasted dollars at a service shop. The process is easy, and you can be up and mowing in no time.

* Socket set (if needed)
* Phillips head screwdriver
* Flathead screwdriver
* Replacement cord

Step 1
Remove the cover to the pull reel. On some models, this will be as simple as removing the 3 or 4 screws set in the casing. On other models, you may need to use a socket set to first remove the upper portion of the engine casing.

Step 2
Locate the 3 metal clips that hold the tension wheel to the pull rope pulley. Gently pry the clips off the tension wheel using your fingers or a flathead screwdriver. Be very careful not to bend the clips out of shape while you do this. Once the clips are undone, pull the tension wheel off the pull rope pulley.

Step 3
Pull any remaining rope to the right to unspool it from the pulley. At the rope's end, you will see a small channel cut into the side of the pulley that the rope is placed in with a knot at its end; this is how the rope remains connected to the pulley. Simply use your fingers to pull the rope out of the channel, and discard the old rope.

Step 4
Unwrap your replacement cord. If the cord does not already have a metal stop attached to one end, tie a small knot in it, and push the cord and knot into the channel on the pulley so if you pull on the cord, the end remains in the pulley and will not come free.

Step 5
Hold the cord so that there is some tension on it, and begin to turn the pulley to the left so the cord wraps around it. Use the end you are holding to guide the cord as it wraps so it forms an even layer on the pulley (not wrapped unevenly to one side or the other). When you have about 3/4 of the cord wrapped, stop.

Step 6
Pull the cord off the pulley (to the right), and guide it up the frame of your Lawn Boy mower to where it will attach to the pull handle. Tie the cord end into the pull handle. Go back to the pulley, and turn it to the left again until the cord brings the pull handle up to the frame of the mower.

Step 7
Re-clip the tension wheel to the pulley. Make sure the clips fit snugly. Pull the cord several times by the pull handle using a quick, sharp movement to set the tension to the pulley. Return the covers you removed, and you are ready to go.

The part number 609457 seems to be available from many online outfits. A couple of web sites are

http://cgi.ebay.com/Lawn-Boy-Lawnboy-Starter-Pulley-609457-Vintage-Mower-/230481451378

http://www.mowpart.com/p226322/Pulley-Starter-S/product_info.html

I don't know, however, what you consider expensive but I think you can get the part for about $20 including shipping.

No, $15.00-20.00 or so is fine. I had been quoted $60.00+; a bit high for a wee plastic disc! (Thanks for pointing that out)

Regardless, I'm sorry to say I can't figure out how to access it. Mine doesn't jibe with the "3 metal clips" scenario above. There is one round central hub I somewhat tried to pry/pop off with no luck. (Being unsure, I didn't push it).

How do I get to it? remove it?

Thanks

I wish I had personal experience with that particular Lawnboy starter but I don't. The manual is available online at the Lawnboy website at the link below and the removal seems(!) to be straightforward (like everything is before you attempt it).

Here is a link that might be useful: Lawnboy Manual

Well you sure called that one! It does look fairly simple doesn't it?

Loosen set screw, slide out starter, replace part, slide back in, tighten set screw. How easy can you get?!

Well, it's underneath so it's not easily accessible and you can't really see it so must mostly be done by feel.

The manual states the key size is 5/32' which, on mine, isn't even close. 1/4" is too large, 7/32" is too small. Something in between would be just right ..something like 15/64" which I don't think exists.
Trying metric, neither 6 nor 7mm are a fit (but then I just noticed one of my keys is a bit twisted).

I'm not really sure what's going on (Are there any metric parts on Lawn-Boy?) - maybe someone replaced the original setscrew with something else?

If you wondered how something that seems to be so straightforward could not be, here's how.

I still haven't been able to finish this. Because it's underneath I can't really see it too well. Could it be that it isn't even really a hex key?
I can't get anything around the outside of it either.

If I cant figure this out, I may have to remove the motor from the deck to access it - which I'd rather not do. What am I missing?

Have you removed the shroud? It shoud be easier to access the starter then. Also, that model was made from 78 to 83 and it looks like there was a change in the starter spring design at some point.

Yes, I removed the shroud and whatever else I could. It didn't help too much.

I suppose the real issue isn't so much not being able to access the set screw. I have accessed it with a bunch of them the problem is none of them fit. The real issue seems to be seeing why nothing fits: wrong size hex key, stripped out, not an Allen but Torx or.. etc.

For what it's worth, based on Model/Serial numbers, according to the Toro Master Parts Viewer, mine's a 1980

There it's listed only as "603345 SET SCREW" with no head type

Here is a link that might be useful: {{gwi:132139}}

I took it apart again, got a mirror and light underneath and it's no surprise why none fit. It looks as though it once may have been a hex head but now, basically round, it barely resembles one.

I thought I may be able to turn it with an EZ-Out without much success.

I already attempted to access it from below by removing the motor from the deck but a broken MOWER DECK BLADE ADAPTER put a snag in that plan.

I have the exploded diagram but can't really tell based on that alone, will it be possible to, leaving the motor attached to the deck, remove sufficient parts in the surrounding area to be able to get pliers or vise grips around the outside of that setscrew?