Pretty sure this is the issue with some play in my forks, and was hoping it would be a simple case of removing the old ones and tapping new bushings in. But some quick reading this morning suggests there might be more to it? Anyone done this at home without the expensive tool?

Lyriks have the power bulge to fit bigger bushings in. You will need new lowers I imagine.

Edit: Try an oil change. The bushings need that thin layer of oil.

Is the play in the forks only at full extension (ie unloaded) or is it there when compressed too?

If the former and only a little play then that is completely normal and needed for the fork to actually work at its best. If the latter then something is not right and I’d suggest getting them looked by TF Tuned.