First off the calculations from the manual always. The condition of the engine and the mixture: find the best lean before taxying (there will always be an argument whether you should then adjust to rich of this) to ensure the plugs remain clean. The only way of being certain the engine is/will achieve the book figure is by performing a static power check having positioned cross wind at the hold. The manual should give you the figures but if a special technique is required then how to do this. Yes, take off leaned at a high and hot altitude but also maybe at sea level if the temperature is abnormally high - i've had to do this in the past even in the UK. Follow the manual short take-off technique. Climb path obstructions/hazards above 50 ft asl should also be calculated.
I've always calculated the decision point using: at 1/3rd of runway expect 2/3rds of the take off speed and the appropriate achieved RPM. This will following an abort give another third to stop plus another 1/3rd for safety. I don't know what a "flukey" tail wind is. In the conditions you describe a tail wind should be a no go (there may be upslope/downslope conditions that could justify taking-off downwind. If this is the case advice from local experienced pilots should be sought, there may be other factors to consider.