alumpkin - I can appreciate your situation. Frankly I believe that the concrete (without the base plate) will carry the load, but it will probably be virtually impossible to prove it. Even though the 6000 psi load exceeds the theoretical (3000 psi) concrete compressive strength, it is like comparing apples and oranges.
What you describe sounds like a point load, applied to a small, thick area, with that area is confined by a relative large mass of unloaded concrete. The column might pulverize a token amount of concrete, but it is certainly not going to "drill" thru under the stated conditions.
By comparison the 3000 psi concrete value was arrive at by the method that we all are familiar with - "crushing" an unconfined cylinder that fails by more or less "spliting open sideways".
With that said, I agree with the others that you should "do something". Your idea of grout inside the member sounds like a very reasonable, cost-effective appoach. jmiec brings up an excellent point about not depending on friction. Perhaps you could drill the tube wall, install thru-bolts in the area that will be grout filled. Then these grout encased bolts can transfer load to the column independent of friction (might take a good many bolts to handle 27 kips, but you should have space within the 4 foot grout length).
P.S. Your H-pile analogy sounds good to me. From first hand experince - during the driving of "true" point bearing H-pile on "hard" rock, the steel ALWAYS "loses" if overdriven (steel deforms, bends, etc. while the rock remains intact).