Ok, time to rethink your problem: firstly, how many pots and pans do you use on any given day:
1. saucepans, about three sizes
2. frying pans (maybe 2)
Ok, the footprint of the saucepans will be the same as the footprint for the lids. You could put a plywood carrier underneath your rack with cutouts to allow access to the handles and store the lids upside down in the carrier.
Your second tier of pans would be
1. specialty saucepans
2. oval fish pan
3. pancake griddle
4. varying sizes of frying pans
These could be relegated to the pantry section on a shelf of their own with the lids installed.
The ones that are a killer for me are
1. mixing bowls. I have some specific for breads, others for pastry, yet others for biscuits etc and then my wife likes making cakes and fruit upside down cakes which require different cooking vessels. My wok resides with my large steel bowls and pizza pans.
2. I have a rather large collection of pie plates (tin, steel, glass, etc.) I use them to freeze TV dinners and to makes pies and freeze them.
3. the real killers are the electric appliances. My mixers (2), food mill, quern, various grilling implements, deep fat fryer (but that's on the way to the garbage, I've found a new way to make chips ;-) ) blender, toaster, and those are the constant use ones.
So, maybe ideas to solve your problem might also help solve mine.