Very interesting Sunni. I am getting into growing vegetables (having grown tomatoes, peppers, eggplants in the past), so your feedback is appreciated. If I need to start anything inside, I'll probably try this method first. For some reason, I did not have any germination from eggplant seeds even after more than two weeks. I did one set of seeds with paper towel and the roots did stick. Have not had that issue with coffee-filters, especially moist ones. Californian, I have noticed when I could not get to transplanting the sprout in time, the seed-leaves separated from the seed heads within the filter. I also tend to bury the sprouts almost completely with just the seeds head showing, when I transplant them and the seed heads separate nicely. I just leave the seed coat alone. So you should plant as soon as the seed has sprouted. If you go to the post linked with the first post, in the 3 or 4 the response, the poster shows images of the process. The last image would give you a good idea of when you can transplant.

The heat in a compost pile is produced by bacterial activity, the more active your bacteria are the more heat is generated and there are at least three different species of bacteria active depending on the temperature, those bacteria that work to get the temperature to 100 degrees stop about there and another species takes over and gets the temperature even higher. The heat is an indication of bacterial activity but it has little do do with the bacteria that function in your soil aiding in disease prevention. Many bacteria, if allowed, will develop immunities, or a means of attacking disease pathogens. You find this happening in your garden as well as in the compost pile, indicating that the heat generated during the digestion process is not required for those immunities to develop. Once again, by the time you get the bleached paper what was used to bleach that paper has been washed out and is no longer in the paper.

I have no idea why Bounty would not compost. Have you contacted them about why their ingredients or processing would result in a composting resistant product? Most curious. We've discussed Organic composting before here, a bit (I capitalize Organic when referring to chemical-free, etc. vs. 'organic' which refers to the organic matter we put in the compost pile). There does not seem to be much info out there on it. We often discuss topics such as paper inks, pesticide residues on grass clippings, etc. To me (and I know you didn't really ask for opinions on Organic composting), the real decision point is a trade-off between composting something and landfilling it because you don't want to. First I reduce and reuse, then decide whether to compost. We only use about 3 rolls of paper towels a year at our house, because 'reduce' and 'reuse' applied to cleaning means reusable rags, sponges and towels. The cheap towels seem to compost fine. I'd be interested to hear more on what you find out!

I can't imagine it would hurt anything, so long as the pile didn't get too soggy. I rarely add any liquid (maybe a little urine) to my pile now that it's up and running. I suspect those UCGs will have plenty of moisture still left in them to overcome the dry paper towels. If not, then using the coffee seems like a sensible thing to do. You could always brew some compost tea or add a little to your watering can.