Seat post suggestions
 

My bike has a short 2 1/2" or 63.5mm of seat post sticking up from the frame. With so little of the seat post visible, there isn't much room for flex. Right now, I'm using a Thomson Elite (0 offset) seat post, but am thinking about buying a carbon post. Has anyone found a seat post that is comfortable with only a small portion of the post showing? Would I be wasting my money on a carbon post?

You would be wasting your money.
It would have to be something like the Specialized CG-R post that has some proper compliance to make a difference.
Or a suspension seat post like a Thudbuster or Cirrus.

OP only has 2.5" of exposed seat post; not sure there is enough length for the mechanisms of the latter two posts. Also not sure that the Specialized CG-R can be clamped that close the dampener, if it fits at all.

Frankly, IMHO, you'd be hard pressed to actually feel the difference between CF and aluminum seat posts no matter how tall they are. I think any supposed benefit is long lost among the other "noise" of saddle comfort and fit, frame design and especially tire size and pressure. I think I'm an outlier in that opinion though.

You would be right. Checked my Cirrus body float seat post and it is around 4.25" from seat rail to the post itself.
Don't know what sort of bike fit the OP has got that his seat post is so short.

That’s where titanium comes in. A tall stretch of Ti can be quite springy, and is my favorite post material. I wish Ti post maufacturers would do more with anodizing; I really cannot understand why they don’t do black, in particular.

Anyway, for the OP, yeah, with such a stubby, little post extension, there’s nothing a material swap will do in the seatpost.

Sounds like a too big frame with the saddle shoved forward to decrease reach. Maybe a frame that fits is in order.

The earlier carbon fiber seat posts have a perfectly round cross section and are designed to be as sturdy as aluminum. Newer ones (e.g., Cannondale Save, Canyon VCLS) have cross sections that are designed to flex, so you can definitely feel a difference compared to an aluminum post. But they require more than 2.5" to work.