Hi, Neil; I'm not sure what the question is(?)...
Are you looking for a way to remove the old wood? Or anchor the new wood?
If the new wood is bone dry when you install it, a simple light pressure should be all that's required to seat it. If it's wet, don't. It'll shrink, and that's where the weeds will set up shop.
If the question was how to remove it, I'd set my saw blade a 1/4" less than the original depth and run a kerf right down the middle...then split either side off in towards the kerf.
I can't see any reason for there to be any nails in it except for the junctions. Use a demo blade (just in case) and you're good!
The old stuff didn't look that bad in the pictures; is it worse than it appears?
Neil, you might also consider giving the new wood an allover coat of a preservative stain before installing it. Concrete is really hard on wood; I think it's likely the high pH, and it reacts for a very long time, hence the protective treatment.