This isn't really an answer to your question as asked, but it isn't really just a comment either. The "simulate paper color" option probably isn't going to do nearly what you want. It's a bit heavy-handed, to say the least, and while it can be occasionally useful for perceptual purposes when preparing an image, if you could manage to save it and print it to another medium, you'll find that your "whites" in the final image are a lot darker and more colourful than they are in the target image. The blacks/darks for matte media soft proofs also tend to get dragged up a lot higher than they should be when that option is active. Again, that's useful for perceptual purposes while working, but not terribly accurate.

Something I would try is taking a screen shot of white with the proofing option on, just so that you can sample the resulting colour. (If you try sampling directly from the image, you get the underlying real image colour, not the soft proof colour.) Somewhere between that colour and white there will be a colour that more-or-less accurately represents the medium the image was being proofed for; the average of that colour and 255,255,255 will probably be pretty close. Create a solid layer of that colour below your image, then set your image to one of the darken modes (multiply will probably be best). You may have to fiddle with the black point just a touch to get a good match.

Yes, it's all eyeballing, though you can use a screenshot of a soft proof and colour sampling through the info panel to assist you in the process. You should be able to get something that's indistinguishable to civilians, other than the fact that one picture has a canvas texture and the other does not. The only way I can think of to get numbers-accurate is to use a reflected-light colorimeter and test prints.