That it doesn't surge at idle is a good sign. What do you mean cold blooded, can you elaborate.
Main problem seems to be the flat spot, can you recreate it on the center stand by just turning the throttle. If you can it may be lean and some more diagnostic work needs to be done. One area of concern would be the accelerator pump. However, if you can recreate it on stand by just holding the throttle steady with the engine breaking down it is likely to be the lean fuel condition.
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