For such a lightweight machine,there may be other factors than backlash.You may well be pushing it harder than it's rather light construction likes and a few things could be flexing-which is a different situation.Have you tried cutting those discs with an initial diameter of 18mm and an onion skin layer at the bottom,prior to going back and reducing them to the final size with several cuts at modest depths?
To be blunt,those machines are of limited use if you intend to cut anything very substantial as the round rails flex and the gantries are less than rigid.The backlash in the screws is fairly insignificant by comparison.You can get things made but only if you take it very gently,it will lead to disappointment if you try to use depth of cut and feed rates that apply to industrial level machines.
Photo carving may be a way of gaining experience but it will take a long time to finish a cut.My only attempts were done using the inbuilt program generation capability of LinuxCNC and worked out OK.I don't have experience of any other photocarving software.You may be able to create some files from bitmaps using F-engrave-if it has a post processor for your control.