The sandles might have had something to do with it! But I agree, I ride my commuter to work with regular pedals and it feels like I'm getting only 60% power. Too much time on the rollers.

Yeah, as soon as I'm not clipped in I feel goofy. I rely a lot on using the upward motion of the pedal stroke, and without it the whole motion changes for me.

+1, you're not alone

This isn't what I want to hear. I am going to fly back to Ohio in a few weeks to do a triathlon on a borrowed bike. I planned on leaving my pedals and shoes in Florida and just strapping my running shoes into the non-clipless pedals.

Ship 'em!

I have flown with my pedals and shoes in a carry on. It was worth it to me... they don't take up that much room. If you are checking something it's even easier!

I ride my bike w/o bike shoes but just for a short ride and it does feel odd.
If you are using toe baskets you will be better off than nothing but ideally you should swap out the pedals and shoes at least.

You just need to make sure you have your foot positioned properly over the bedal body and you won't feel too awkward. You'll likely lose a bit of your power output for a given effort, but it just means you need to push a little harder. Toe straps will help you feel more normal and give you a bit better efficiency, but you'll still be losing power to the compression of foam in your running shoes. I ride into work on standard pedals with leather soled shoes every morning, and with the exception of the hills I have to crest, once you get to a nice cruising speed you don't notice the difference too much.
One plus to this set-up is your time in T-2. You'll be looking at sub-15 sec.