You didn't say how many miles you have on your engine - but here's a run down of what you may be faced with.

The "carbon build-up" on the top of pistons is a normal by product of the oils and solid deposits that will, over time, find their way into the combustion chambers of any engine. As your engine wears, the rings and valves allow oil to pass and it coats the piston. The build-up doesn't burn clean and continues to accumulate. Modern gasoline may contain additives to help this condition, but eventually all engines develop this condition. High speeds and long, hot run times help, i.e., better to drive a lot of freeway miles than a few "around town" trips.

The lip you are feeling is called a ridge and it is a result of the piston ring wearing the cylinder down. Again, normal in all engines and eventually results in a loss of compression along with allowing oil to pass.

You may be disappointed rather quickly if you rebuild just the top-end (heads) of your engine. New (or rebuilt) heads will have tight seals and valves which will cause pressure to be forced back into the cylinders (past the worn rings) and cause undue pressure in the crankcase. This will be readily visible as smoke coming from the breathers

I think you would be well served to take the time and spend the money to do the entire engine. The results will be better and in the long run, you'll be a lot happier with the performance of your car.

Good luck and let us know what you decide.
Glenn