I'm gonna be slightly differing in my opinion. 100% agree with swapping pedals - you might never switch to clipless, but at least you're riding!

Now, about being able to reach the ground from the saddle... that's where I'll differ. Most people can't touch their toes - they have to rise up off the saddle and step down with one foot as the bike slows - in front of the saddle. So when you're stopped, you're straddling the top tube, not the saddle. I would love to say to practice this with the seat in that lower position, but it's actually much harder to do this move when the seat is too low. Do you have a trainer that you can use to practice this? If not, go ahead and lower the seat until you're more confident on the bike, and maybe practice stopping this way, even though it takes more leg strength.