What you should do to protect it would be to put it in a steel shed (any thing conductive that surrounds it creates a Faraday cage) A Faraday cage grounds out all the exterior electromagnetic interference and protects what's inside.
Unfortunately your wooden and rubber protection would be pretty much useless frying any circuitry in your generator.
The damage of an EMP is just like any wave based disruption in that it is the strongest nearest to its generation point. A simple steel screen mesh can protect your electronics even as simple as a chicken wire cage as long as your electronics don't touch the exterior conductive metals.
I would recommend covering as much of your sheds interior with sheet metal. (rust prevention) Shield the floors for good measure. Shouldn't cost more than $100 in steel depending on how big your shed is.
Creating a conductive box and insulation inside will keep your electronics protected. The Faraday cage has no theoretical size limitation.
The biggest threat would come if you have an extension cord plugged in, the longer the cord the more energy it would send to the generator. One of the best ways to protect against the pulse would be to use Metal Oxide Varistors (MOV) across the receptacle on the generator. They only cost about $1 each if your voltage is rated at 120v buy a 220 v Varistor. In fact it may not be a bad ideal to use them to protect all you equipment.
I ask because typically when someone thinks of EMP they think of one from a HAAB. While it's effects would be far reaching. The energies seen on the ground are not that great. So it will really only affect infastructure and some very delicate unhardened pieces of equipment. Things like cars and small generators wouldn't be as heavily affected as many think they would be.
Now a purpose built devise used on or near the ground would have a greater effect, but would affect a much smaller area.
But anyway. The wire mesh Faraday cage would protect it pretty well from all of the above.