Just one thing with the Loctite Mike: you will need the high temperature type, not the ordinary type. The regular stuff would be fine for an inlet valve guide but not for exhaust. (Of course the guide only came loose because of the high temperatures reached by the exhaust valve guide).

I would use a lathe to make the valve guide tool, mainly because it lets me get square ends and a straight, central hole, in just a couple of minutes. However if I didn't have the lathe I'd use a drill press.

The parts list shows a valve stem seal, and does not specify "intake only", so if there are marks from one having been on that exhaust guide, it seems your engine has been dismantled before. Here is the part:
http://www.2lcstore.com/honda-small-engine-valve-guides-stem-seals.html

I don't know the history of your engine, but it does sound as if the guide has moved up, pushing off the stem seal, and somebody has just taken off the retainer, removed the stem seal, and put the retainer back on, thus keeping the mower running a bit longer until the guide moved up further.