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The speed look about correct for me. I have found a web site that will help you to calculate the speed.
This should assist you but if you need more information please do not hesitate to ask me.
Yes there is a solenoid inside the transmission that select the overdrive. If when you say you can only feel three shifts up then something must be amiss. Usually the solenoids get sticky as the fluid becomes tacky with age. The guy that has done the service would have stripped the transmission pan of and drain the fluid but not remove the solenoid bank to clean it.
Yes one can repair it by taking the pan of and then the solenoid valve bank. The time will depend on what the problem is. There cloud be a wiring problem inside the transmission or sticky solenoids or bad contacts meaning cracked or loose soldering at the plug but all in all it should not take more than two hours.