I tried setting up a brand new one in Cakewalk by Bandlab completely from scratch, added some drum tracks in and then recorded some guitar over it. When I then listened back to it, the whole thing sounded horrible, it was a bit distorted, but mostly it had clearly recorded with significant latency, the guitar was way out of time with the drums. I saved that, opened in Sonar Artist, and could record the guitar fine and it sounded good.
So I flicked back and forth between the two checking out all the settings and things and I finally figured out the difference. And I'll record it here so if anyone else has any such issues hopefully they can find this. Sonar Artist had the Driver Mode set to ASIO, but Cakewalk by Bandlab had it set to one of the WASAPI options (can't remember if it was exclusive or shared). Anyway, once I changed this it fixed everything. I could record without the latency, and when I opened the project mentioned in my original question it played fine without the issues.
Glad I wasn't just setting up Cakewalk by Bandlab without the reference of Sonar Studio, as I can't imagine I would have had any thought that I needed to switch from WASAPI to ASIO.
Chris Kettlewell's post in Opening Sonar Artist project in Cakewalk by BL doesn't play properly was marked as the answer