Nick
I had this on my Aero S1.
Battery was always kept on trickle charge ;permanent and then timed intervals - (but thats another story!).I didn't always get the dreaded
'click' but often enough to be annoying.
I fitted a new Odyssey battery (I think I'm on my 3rd!) and it did improve a little ,but always reverted.
Having some other work done I bit the bullet and got the starter motor replaced and ........end of problem

It now fires on the button.I believe the starter gets well 'cooked' from the engine heat, coupled with (perhaps) a potentially degraded earth and a battery just off top performance and Bingo

I know you said the starter has been replaced but, was it a decent unit - lots of poor quality re-furbed and
Chinesium copies out there.Also, I'm not sure how long their shelf life is in the un-friendly environment.
Worth checking before investing in a new battery.....
James