You’re talking about just getting them turned around correctly so that you can clip them in, or actually getting the cleats to engage? If the former, they will hang upside-down by nature (or at least my Look pedals do, and I assume it’s the same deal). What you want to do is catch the front of the upside down pedal with your toe, then move it up and forward so that the pedal is rotated into the correct position and you can click the cleat in. It’s one of those things that’s complicated until you get the motion down, and then you wonder how you ever failed to do it before.
If you’re having difficulty getting the cleat to engage, find the hex wrench that fits in that hole in the back and loosen it a bit – it won’t hold the cleat as securely but it will make it easier to clip in.
Plus one on what dmg said. It sounds like you’re not be served well by your pedals.
Speedplays are nice but gum up easily and the large cleat is not great for walking.
Thought about getting MTB shoes and pedals? Crank Bros pedals might work well for you too. I am not a big fan but you could get the road model and still wear your current shoes while getting an easier to use pedal.
After years of trying to settle on a pedal solution (for like 6 bikes, give or take) I finally just went all SPD compatible. I have mountain pedals that clip in from either side, single sided road pedals, and dual pedals that have one side for street shoes. Plus the shoes I have are totally walkable.
To actually address your question, get some compact mtn bike pedals that clip from either side.
You’re right on with the former dmg. They seem to hang upside down more-often-than-not. I have SPD pedals (clip on one side/pedal on the other) for my commuter bike, and I never have problems. Just thought perhaps I was missing an adjustment somewhere that would keep them from flipping over. It’s not the end of the world, but I hate fumbling around in the middle of traffic.
This is the first time I splurged on a nice road bike, so I generally only use it for long group rides where I’m not concerned at all about walking. I guess it sounds like I need to work on my technique.
While I’ve mastered both styles of pedals I stink a moving between them. I always spend a month at the start of road season and a month at the start of cross season fumbling for whatever pedal I am going for.
Since you have MTB shoes and pedals I’d really suggest moving to that on your road bike as well.