My coneflowers curl downwards as they grow up but face up while in bloom so I wouldn't worry about them.

The yellow leaves on the catmint is a sign of root damage, more than likely too much water so rise it up first.

If your original soil doesn't drain well you should always plant on top of it and build mounds of good soil around the plants (sort of a raised bed without walls). If the area has some slope to it you can also dig little trenches to drain the bowls of clay under the plants. Sitting in water is bad for most plants.

If its been as wet as you say these guys have probably not grown a lot of roots so go ahead and dig them up. Keep in mind that the roots will eventually be longer than they were in the pot so you want to really mound them up high. Also keep in mind that both cone flowers and catmint don't need extra rich soil, just normal garden soil will do. Some of them bloom better in poor soil.

I would say you have two choices.
1. Leave them in the holes filled with water and watch them die a slow death.
2. Replant them higher and give them a fighting chance.