Genghis I think you were correct to continue with the approach as at least one of you was where they were supposed to be. I also agree with Dufwer that turning away when unsure of the location of the PA-28 could have been a turn into him.
I had a similar problem flying into Cranfield last year. I was carved up by a Tomahawk whilst on final in an Auster. I would have thought I would have been easy to see as I was slightly above him when he turned onto finals 100' in front of me. If I had been in a low wing type I wouldn't have seen him at all.
When I flew a Cub, I routinely flew as tight a circuit as possible (within published noise abatement etc procedures of course) and then carefully slotted myself in on the base leg amongst the C150s etc which were imitating Vulcans
I felt it was better that students in the circuit didn't have to think about how to avoid the slow yellow thing in front of them and I felt a whole lot safer too.
Best of all was the red Hunter which came whistling up from the South coast of a certain island to do a low pass over a certain airfield there. Not a problem as I could see him coming after hearing him call the A/G operator. I would have not been concerned at all but, after calling the said A/G Op and telling him of my position, the A/G Op told the Hunter driver that there was no traffic in front of him. Yoiks
The Hunter passed 100' below and 2-300 yds to my right. As I was silhouetted against the sky from his viewpoint, I'm sure the Hunter bod saw me..........