This is probably a mega stupid question (there are reasons). But for a bike with 142mm rear axle, I take it the gap between the dropouts should measure exactly 142mm across?

When you put the wheel in and do up the axle it will. Mine are slightly wider on one and much wider due to frame flex.

http://www.pinkbike.com/news/12×142-explained.html

Hmm. Can’t get some play out of my rear wheel. I think it measures 147mm or so across without wheel in. (Enough that it requires some care to ensure the wheel sits in the dropouts before putting the axle in).

Sounds like it might not be that then.

The problem is really strange:
When the rear axle is tightened reasonable tight. I couldn’t get it any tighter – Play in rear wheel (noticeable even when holding the seat stays)
When the axle is loosened quarter of a turn – No play

Uhhhh, Second thoughts – That might happen if one of the main pivot bolts was loose. Ugh tomorrows job.

On the plus side you only need to find an extra mm to be boost compatible.