I have a couple of ideas that you might try with the original candles (in case you haven't already).
1. Check where the bottom end of the spindle is. Is it on its intended pivot point? My pyramid has a little glass "button" with a slightly concave upper surface that the end of the metal spindle is supposed to rest on. When it's on the glass button, it spins very freely, but if it wasn't, there would be a lot more frictional resistance (not to mention the metal spindle possibly tearing up wood on the base of the pyramid). If yours has gotten off of its intended pivot, that could be why you need some extra airflow from bigger candles to get it spinning. If for any reason it doesn't spin easily when you turn it by hand, or it stops really quickly after you spin it, then the problem probably isn't the candles.
2. Are the blades of the fan fixed or do you insert each blade into the fan individually? If they're separate, try playing with the angle. I think a shallower angle (i.e., with the blade surface closer to horizontal) might help it get moving with the smaller candles. Be willing to wait a few minutes to see if it gets moving or give it a nudge to get it started and see if the candles keep it spinning (the shallower blade angle should catch more of the updraft from the candles, but less of the updraft force will be pushing it in the "spin" direction, so try a few angles).
One thing to remember is that it takes more force to start the thing spinning and speed up the rotation (in technical terms, to accelerate it) than it does to keep it spinning at a constant speed. Since you can't "turn up" the candles at the beginning and then turn them down once it's up to speed, the candle size and position has to be designed for the constant speed. That means it's going to be slow getting started, especially if you've just lit the candles and they're still warming up and melting enough wax to get a good flame going. It might just need a little more time or a nudge.