Hi Connie,
" Would it be okay if they stayed in the ziplock bag in the paper towel until after I'm home? Would be close to 3 weeks by that time. "
I am sorry to say that your zinnia seedlings will not be alright on a paper towel in a Ziploc bag after 3 weeks. They will be trying to develop true leaves by then, and suffering from a lack of light as well. The Ziploc/paper towel thing is suitable for germination testing, but has serious disadvantages as a way of starting your plants. It is common for the roots to become embedded in the paper towel and you wind up trying to pot pieces of paper towel.
If you know someone who could babysit the pots, that would be one solution. Otherwise, set the pots in a pie pan of water, or a tray of water. If you have a tray, you could put it under a humidity dome to slow the evaporation of water from the pots.
Since a single packet of zinnia seed is all that is at stake, you can always buy another packet of zinnia seed and start over after the funeral.
ZM