I must admit I do worry a bit about you clipping out both feet.

The thing is that you then become quite unstable if you think about it. Once both your feet are unclipped (and you tend to remove them from the pedal when you do that so you don't accidentally clip back in) the only things touching your bike are your butt and your hands on the handlebars. Your handlebars move relative to the bike (duh! that's what they are supposed to do) and so unless you have a very strong core, you can tend to be a little unbalanced once you are reduced to one fixed attachment and two moving ones. Your body could wobble a little bit and it's fall time!

What I suggest is that you work out which foot you naturally have at the top of the pedal stroke ready to get started and which foot you push off the ground with? Is there one that you favour more than the other? I realise over time it would be ideal to be able to cope with either, but maybe you need to find out which is your preference and use that at least for the first little while until you have it down.

Then once you have worked it out, practice unclipping the foot you push off the ground with, and develop a little routine around it that you can commit to muscle memory. Say... gently apply the brakes to slow down, unclip the foot (while it's at the top of the pedal stroke) hang that foot down, little bit more brake, lean the bike (and you) a little that way and put the foot down, lift the other foot to top of pedal stroke (because then you are unlikely to lean that way and fall over standing there, and also you are ready to go again).

I just think that the more things you can have attached keeping you and the bike stable while you do this, the better off you will be.