I think grabbing for the paintings in the bag was part of his plan because something like that would otherwise be uncharacteristically rude behavior for Columbo. Normally he is "annoying" to the suspect but he is polite, the way he stuck his hands in that bag and tried to grab the paintings was very brutish. Not only was it extremely rude but he could have ruined the paintings, I think he would know that so wouldn't just grab them if he didn't suspect what they were and wanted to get his fingerprints on them.

But he didn't know when a safe time would be. He had to find that contact lens and get rid of it before the police searched and found it. They could have searched that night and then all would be lost. Sooner just seemed better. I know he's was in a panic isn't a small "but..." it's a very important point. Columbo planted a seed he couldn't ignore even if he expected it may be a trap.

The ending isn't really the "cart before the horse". It's that Peter has a great memory and is prepared to testify against his girlfriend as a witness. I expect he'll have to demonstrate that memory but he should have no trouble. It's not really an episode of logic as many of the best are some Columbo episodes, like this one, are episodes of emotion.