Any suggestions on what to shoot into? Maybe the soaking wet newspaper idea? How much penetration should I expect?
Newspaper is what I use. In order to get consistent, repeatable results, I remove all the flyers, tv guides, slick ads, and anything besides plain old newsprint. Let it get absolutely sloppy, saturated wet, for at least a 24 hour soak. Put it into whatever kind of rack you want to use, so that the bullet will strike straight into the face of each sheet. I don't compress the sheets together, as this would be hard to exactly replicate. The paper is just stacked in the shooting box, then the box is tilted back down to a horizontal position.
Penetration to the vitals is what does the job, especially in slow moving cartridges. If your trimmed jacketed bullets had a wide meplat, they'd be fine with no expansion. It's uneven expansion, and tumbling, that I would worry about in your experiment. Maybe, while that bullet is still in the trim die, you could try giving the nose a whack with a punch, to make a hollow point. It would be easy to make the punch so that it only goes in to a set, uniform depth. Maybe you could experiment with some of the bullet nose punches made for muzzle loader bullets. Trying to anneal jackets, or otherwise enhance expansion, seems like it's more work that it's worth.
I like loads that go through at least 18"-24" or more of soaked newsprint, but that's with elk in mind. Expanding bullets with high sectional density can reach this, and non-expanding bullets will easily punch far deeper. Penetration in meat will be deeper than in newsprint.
Good luck, this sounds like a good winter time experiment.