Do you want a composite pool cue?
Or do you want a "magical material" that is like wood, only much better? And then you will figure out how to make a pool cue out of it.
As you probably know, you can make a hollow metal tapered cylinder which is hollow enough to float. This is the design part of materials utilization.
Wood uses internal voids to create this low density and oriented fibers to create the high elastic modulus.
It is possible to make something approaching or exceeding the modulus you cite with a density not much larger than 1.0..
Presumably, somebody could figure out either:
1) how to add controlled voids of void containing fillers to get closer to what you want.2) how to use shape, such as a tapered hollow cylinder, to achieve the desired structural response.
How much money do you have to achieve your goals?
Remember, the advanced composites took over most of the bamboo fly rod market, and never made a material (as opposed to a rod structure) that resembled bamboo in the slightest way.
I would learn this fly rod lesson quite well in making new generation pool cues.