The 6-8 minute loss is almost always a setup problem, not a solving problem. Here's the decision tree I used in JEE:
Step 1 (10 seconds): Read the question and ask — does it ask for a final state quantity (velocity at the bottom, max height) or a mid-motion quantity (force, acceleration at instant t)? If final-state, jump to conservation. If mid-motion, FBD is mandatory.
Step 2 (30 seconds): Identify constraints — rolling without slipping? string-pulley constraint? These give you 1-2 free equations for free. Write them down before doing any physics.
Step 3: Pick your axis once, then commit. Most time loss comes from re-picking the rotation axis halfway through. For rolling problems, the point of contact is almost always the cleanest axis — instantaneously at rest, so τ = Iα with no extra terms.
Practise this on 10 PYQs back-to-back with a 4-minute hard cap per problem. You'll feel the difference inside a week.