Have you ever seen a self-watering tray? It's a waterproof tray with a raised "shelf" over which a synthetic felt material is laid and draped sown into the tray. The tray is filled with water and wicks moisture up to the top surface. You put your pots or seed trays on top and the idea is that the soil in the pot will wick moisture up as needed.
A lot of them come *with* seed growing trays, but you can buy them individually as well. You can also google search for DIY versions. (I suspect commercial versions won't sustain your plants for 2 wks, so you might want to go ahead and try to make a larger reservoir unit)
You can also try to adapt house plant self waterers, though with seedlings the bottom watering mat version would probably be gentler.... Whatever you use, test and make sure it works before you go away. I had a commercial version of the seed tray waterer that didn't work right until I realized I'd set it up wrong.
Oh, come to think of it, I just saw a version of the self-watering tray in a catalog that is intended for use with grow bags. Much bigger reservoir.