Can I use something like the Lami Texalium or one of the other brands out there to make a handle extension? Is the stuff strong enough to make a 18" extension for a lighter surf rod, given the forces that will be generated during casting?

That depends on how light and how much force you're talking about. Is the Texalium at least as stiff and strong as the butt section of the blank? If not, then I wouldn't use it for that purpose.

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I've never actually handled a piece of it. Does anybody out there know how stiff it is? I would want it to be very stiff given the way I am thinking of using it.

Marty,
It is very, very stiff. It is somewhat counter intuitive but stiffness is primarily a function of diameter and length and wall thickness affects it very little. Stiffness increases at the 4th power of diameter (twice the diameter will be 16 times as stiff). Most of the Texilium is 1" in diameter which I assume is quite a bit larger in diameter than your blank so the Texilium will be quite a bit stiffer than your blank.
I think that your problem in using the Texilium as an extension is not going to be the stiffness of the Texilium but is more likely to be the strength of the joint between the Texliium and your blank. If the shim that you use is not very strong and the blank moves at all inside the Texilium the joint will fail.

You can use smaller ID GRaphite tubing, but that only comes in GRey/Black color. What Emory said about the shim is really important. I have a rod which I used 1/2" Titanium tubing as an extension in a Fuji DEtachable reel seat. I used an FC arbor, and when I flex the rod the extension bends at a bad angle, as if it is goign to break. I do not use the rod as a result. What I'm pretty sure is happeneing, is the FC arbor compresses when the blank is flexed (it's an 8'8 GUSA Monster rated 30-60#'s, so theris a LOT of pressure on teh joint). Teh shim is only 3 3/4" long due to teh construction of the reel seat.

I hae another light 10# rod which I used a piece of 15mm CArbon Fiber as an 18" extension which the gap was very small and I used standard grey graphite arbors, and have no problems whatsoever.

Actually, the blank I have in mind is the Seeker CSU100, which has a butt size of .965; and the Texalium has an I.D. of .980; so the difference looks to me like 0.015 which I'm guessing would be taken up by 1 layer of D size thread. I also understand that the CSU100 has a "straight" butt section, so am I correct that it will have no taper at the bottom?
The only thing I think I don't like about what I have in mind is the need to use a 26mm reel seat; but on a spinning setup that might actually make for a good grip.

The butt of the CSU100 is much stronger than the Texalium. You need something else for the extension. Wall thickness does play an important role here, not so much for stiffness as the diameter does, but for strength.

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Sounds like aluminum with a twine grip wrap might be the ticket if I go this route.