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The shaper turned at too slow of rpms for the 2 flute router bits
Number of flutes is not the issue. A 3 flute tool cuts at the same speed as a 2 flute tool. It just takes a shallower cut, all else being equal.

The reason shapers spin slower, is that they use larger diameter tool, which give faster cutting speeds at the cutting edge.
Wood needs to be cut at a minimum speed to get a clean cut. Too slow, and the bit grabs the wood and tears it apart, instead of cleanly slicing it.
This is why router bits don't work well in a shaper. They would work best with large diameter cutters, at a minimum of 8,000-10,000 rpm.

If that thing only has a 1/2" arbor, you should be able to use 3/4" bore cutters.
It looks like these comes with a 1/2" spacer or bushing.
https://www.toolstoday.com/shaper-cutters/carbide-tipped-raised-panel-shaper-cutters.html?bore=107
 

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Sorry, but I disagree.
A shaper gives a far better cut quality than a router, and it's due to the larger diameter, not the number of cuts/minute.
Cuts per minute is meaningless without knowing how fast the wood is being fed into the cutter. Cuts per inch would provide more info. Due to it's larger diameter, a shaper is typically slicing through the wood at the same speeds a router is.
A 1/2" router bits cutting edge is moving about 29mph at 20,000rpm.
A 3" shaper cutter is moving at 70+mph at only 8,000 rpm. SO it's cutting nearly 3x faster at less than half the rpm.


Shaper cutters are more expensive than router bits because they are often 3-5 inches in diameter, rather than 1/2" to 2", and can have 3-5x more carbide in them.
 
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