Can I just cut the carbon seat tube, cut a vertical slot for compression and use a conventional seat clamp to hold a seat post in it?
That is unlikely. The inside of a frame is machined/molded to a specific size for the seat post. An integrated post is not finished internally. Also, it is unlikely that the internal and external diameters of the post/frame/clamp would match well enough to be ridden safely.
Seat post fitting is a zero tolerance game, and they are dimension-ed to the tenth om millimeters. You would have to be beyond lucky for that to work out.
I had a similar issue and found that the inside diameter was an odd size. One millimeter is a mile as far as seatpost sizes are concerned. Another issue is that on some frames (in my case a Schwinn) the seat post won't insert past the top tube. This leaves very little post inserted. I settled on a Ritchey WCS mast topper. It will allow for approx. 40mm of height adjustment by using spacers. It is an alloy model that weighs about 17 grams more than the carbon at about 1/3 the cost.