Not sure what you're encountering when you say 'skipping towards larger cogs' , can elaborate more ??? Like at which gear do you start to encounter that ?
Typically, the symptoms sound like a misaligned derailleur or simpler still a mis-aligned wheel. As in, it has not be mounted proper straight on the rear stays. Tried checking on that yet ? As in tyre clearance on all four stays should be even on either side.
This wheel alignment portion, I've encountered a few times on a few different bikes simply because of poor quality light weight skewers. The clamping force was too low on titanium/steel dropouts, resulting on not enough bite (some use aluminium clamp nuts, which are too soft) onto the dropouts which, on hard mashing, the whole wheel just moves on the mounts, and goes out of alignment.
Try swapping out for a pair of high quality clamp skewers or at least one with steel clamp interfaces to see if the problem will stop.
Alternatively, perhaps you can try swapping for a Shimano cassette with the requisite spacer to see if the problem persists ??
Hope the above will help.