I need some advice. I am trying to root some cuttings right now using the baggie method. They are on a heating mat, running on a timer and are seem to be progressing slowly, but no visible roots yet. I leave next week for a two-week business trip. My wife will be home, but I need to leave them more or less unattended for that time. I don't want to leave them in the baggies, so here are the options I am thinking about:

1) pot them up in homemade humidity dome, on the heat mat. Keep dome sealed.

     OR

2) pot them in open containers and ask the wife to water ever few days

Which of these would you recommend, or is there another option?

Of those options I would prefer 1.  Though option 3......shut off the heat mat and leave them for the two weeks at room temp.  You may come back to LONG roots but that is manageable.  There is no reason not to leave them in the bags.  They don't really need aired out.  It depends though on how long they have been in the bags already.  1-2 weeks no problem.....if they have been in the bags 4 weeks, well could be a problem. 

Why the heating mat?, simply place bags in a steady warm dark closet shelf, 2 - 6 weeks later you should have roots in the bag with moist but not wet media in the bag. sealed zips should be fine for a week or two.

even with humidity dome, you have to air out. mold can be a problem. heating mat is a bad idea. that might cook your cutting. asking your wife to water them is also a bad idea. at rooting stage, wrong amount of water can rot the cuttings.

if you are gone for two weeks... if i'm in your shoe, i'll move them to new baggie with barely moist paper towel and hope for the best. clean mold and cut off rotted part when you come back.

What JackHNVA said

Leave in bag. No heat mat. 67 degrees works. Just slightly moist. Come home to rooted cuttings. You can try both methods to experiment but I already did since I go on a ton of business trips and this works best. Best thing you can do is leave them alone.

one of my fig packages sent out, returned to me when I was away for 4 days.  The package was in transit, mail rooms, airplanes, and my cold porch for at least a couple of days... I thought they were dead, upon inspection, I could not believe how good and how many eyes pushing roots they had. My conclusion is that we baby these guys too much.  this package was not open for airation for more than 3 weeks and they are fine... At home, I open for fresh air, inspect mold issues... you know the story... so, I think Jon's method to put in a bag and in a moderate temperature *on top of refrigerator" and leave them alone is the way to go.. but how to stop the fig impulsivity, right?

Being in exactly you situation is why I started using a plastic tote with holes cut in the top for circulation, I keep mine on heat mats..I have thermostats and humidity meters in. Before I started doing this I had mold and fungus gnat problems and i was worried that when I was gone 10 days over Christmas I would be coming back to fuzzy rotting messes... these have worked great.  

This will only be my 2nd season rooting cuttings, but my 2-cents would be to definitely turn off the heating mat while you're away.  If that slows things down while you're away...well, that's not such a bad thing.  Plus, horrible things happen just that much faster when heat is involved, so why tempt fate?
  Again, I'm a relative noobie, so take my 2-cents with a grain of salt (if I may mix metaphors).
Cheers,
Jim

Leave thecuttings in the bag(s) for the moist baggie method at your home temperature which you say is 67F~70F  (no heat mate). This will slow down rooting as well as slow down rotting and mold. Let your wife air the bag(s) every other or 3rd day. This should minimize the work/risk/worry. 
God luck