What Kaye did
"If I'm correct here - He was convicted here for operating a botnet for payment from within the UK, Not for the events covered by the separate German case or the specific Liberian DDoS, these will just be used as evidence for the activities he actually conducted here."
No, you are wrong. The botnet was run from Cyprus. He was tried in Germany - and pleaded guilty - for the collateral damage in Germany caused by his efforts. He was tried in the UK for the Cyprus >> Liberia activity because sections 4 and 5 of the Computer Misuse Act 1990 gave the UK courts jurisdiction.
What some see as a relatively modest sentence reflects the fact that he pleaded guilty at a very early stage - in fact the German courts said he was fully co-operative and it was German police work that the NCA relied on.
NCA also investigated whether Kaye was responsible for DDoS attacks and associated extortion demands on UK banks - but these charges were withdrawn before trial.