A bud of mine picked up a Stevens this summer for gophers. He was talking about stiffening up the forend and mentioned carbon rods too. Same source of ideas, I'd have to bet. Or he was looking at yours.
I'd be willing to go with the microballoons and try it that way. The weight will be not much. The balloons will allow the places that the epoxy has to flex a wee bit of give, while still being relatively stiff.
If you are anywhere that has a Model Airplane Hobby Shop, they would be a source for smaller qty's of microballoons and good epoxy (as opposed to the five minute, grocery store stuff)
If you can track down some 3M 2216, it's good stuff and flexes when cured. But a can is about the same price as the Stevens, so... Maybe not. Looking at about $10 for enough epoxy to do about five jobs, if you buy the small bottle kit. Should be around that for a margarine tub of balloons. Maybe a lot less, depending on whether they are marking up pre-packed stuff, or buying bulk and re-packing it themselves.
I usually stop in the shop in 'Toon town, as I pass through towards Moose Jaw. Handy stop. There is a Robins Donuts across form it.

Hobbyworld, on Idyllwild N., around 36/37 St area.
Good place to stretch the legs out on the way.
Cheers
Trev