We investigate whether structured reasoning interventions improve the strategic economic reasoning of large language models, and whether their effects depend on model architecture. Using Hotelling's linear city model as a diagnostic vehicle, we evaluate GPT-4.1-mini (a standard instruction-following model) and GPT-5-mini (a reasoning-optimized model) under five conditions - an unscaffolded baseline and four reasoning interventions - across eight questions spanning deductive and abductive reasoning, three prompt framings, and three repetitions per condition, yielding 720 individually judged responses. We find a statistically significant crossover interaction between scaffolding type and model architecture (
t(7)=4.79,
p=0.002,
d=1.69): commitment scaffolding improves the standard model (
+0.21) while degrading the reasoning model (
−0.63), and principled separation shows the opposite pattern (
−0.40 vs.
+0.31). Both crossovers are individually significant (commitment:
p=0.040; separation:
p=0.002) and hold across all eight questions with 7/8 directional consistency. Adversarial stress-testing harms both models, with
2.6× greater degradation for the reasoning model (
−1.47 vs.
−0.57;
p=0.038), and the damage correlates negatively with baseline difficulty (
R2=0.36,
p=0.014). We further document a persistent declarative-procedural gap in which both models identify correct strategies at rates far exceeding their ability to execute them; separation fully closes this gap for the reasoning model while no intervention helps the standard model.