MIMF

I bought these carbon fiber rods from Aloft Hobbies. They are 1mm×6mm×1m. While I realize that 1mm is quite thin, and that they resist flexing better in the 6mm dimension, they are still less stiff than I expected. Here is a video of me wobbling it in the 1mm dimension. However, I am able to slightly bend it in the 6mm dimension by hand, although that's harder to demonstrate on video.
https://youtu.be/7Yh0zUhM8Ow
I bought them to run through the neck and body of my instrument, as I want very high stiffness for piano-like tone. I was planning to glue multiple of these together so that they're 2×6mm, or 3×6mm.

When I was shopping online for carbon fiber, I decided that I needed a length of 92-100cm (or 36"-40"), preferably in the upper end of that range. Before I considered this 0.236"² and this 0.125"×0.325" rod from Rock West Composites (cut into appropriate lengths by their service), and also this 0.187"×0.325" from DragonPlate. But those are more expensive. DragonPlate may appear cheaper than Rock West Composites, but they require a shipping quote by e-mail, which ended-up being $46 for me on-top of the $30 minimum order.

I chose Aloft Hobbies instead because it's much cheaper. But they are not nearly as stiff as I expected. I read here that stiffer grades of carbon fiber have a higher "msi". I shouldn't be surprised if Aloft Hobbies are a lower grade, given the lower price, but I don't want to choose the more expensive option if they don't provide specifications to prove that they are high-grade.

Do you think this carbon fiber really is too floppy for it's size, or is this just usual for carbon fiber if this size?

Update: I found here that Rock West Composites standard modulus carbon fiber is 33 Msi, and that this is a measure of "tensile modulus". However, I don't know if Aloft Hobbies has the same or lower.

When I ordered from Aloft Hobbies, I felt like probably any carbon fiber would be good enough.

A ratio of 6:1 depth to height makes it tough for a beam to resist Y axis bending, as it doesn’t have enough X axis material to resist buckling (I may have my axis swapped, but hopefully you get the idea). If you laminate several of those 1 mm strips together and can get closer to a 6:3 or 6:2 ratio I bet you’ll be surprised at how much stiffer the resulting member is.

If you constrain it in a slot so it cannot "wobble" you will gain all of the value of the 6mm stiffness, whatever that might be.

You'll get 4x the stiffness by going to a 12mm wide assuming you have the depth in the neck. I use 1/2" x 1/8" pultruded spars and embed 1/8" into the bottom of the fingerboard which makes a very stiff assembly. A couple of 1mm x 6mm profiles probably won't make any measurable difference in most necks. Call Allred and see if they have Canadian distributors, that should save you a bundle in shipping at least. Pultruded CF is a pretty ubiquitous product.

Josh House Canadian Lutherie Supply has 1/8 x 3/8 pultruded strips. I order mine directly from Allred (Dragon Plate). I usually order 6 or so 4 ft. lengths. Makes the shipping cost worthwhile.

" I want very high stiffness for piano-like tone"

Why do you feel this will give you a piano like tone?