We report a system for the LM-KBC shared task under a strict single-repository parameter budget of 32B, which rules out both model ensembling and scaling to a larger model. Starting from a rationalized chain-of-thought (CoT) pipeline that reached macro-F1 0.522 with Gemma-4-31B-it, we show that swapping to a smaller, differently-trained model (Qwen3.5-27B) under an identical pipeline recovers 24 percentage points of exact-match accuracy on a purely numeric relation (surface area), while costing accuracy on relations requiring broad factual recall. This shows that parametric knowledge coverage, not reasoning capability, is the limiting factor at this model scale. We then present four negative or reversed results (self-consistency sampling on numeric relations, a confabulation-guard prompt, and two cases of non-comparable validation splits) as diagnostic evidence for why scaffolding choices that help one relation type hurt another. We introduce CoRe routing (Construct versus Recall), which assigns each relation to CoT or direct answering according to whether its answer must be constructed or merely recalled. CoRe reaches macro-F1 0.548 on validation and 0.541 on the test split.