The delayed upshifts will be caused by either to much throttle pressure or not enough governor pressure.
This could be caused by a few different things. Your upshifts are controlled by governor pressure and your downshifts are controlled by throttle pressure and here are the things you should check!
1-Check your throttle valve cable on the driver front side of the transmission. It connects to a throttle valve lever. When the gas pedal is up the lever should be all the way forward and when you start pressing the pedal it should start moving rearward, The lever has a return spring on it to return the lever to the front. Check this for binding/sticking and make sure it works freely!
2-Your governor pressure has to be monitored with a scan tool. In drive stopped the governor pressure should be 0psi and as you start acceling the pressure should rise. I use a scan tool along with a pressure gauge hooked to the governor pressure port on the right side of the transmision then I compare to make sure the sensor is working properly. Governor solenoids are the most common part that fails with these 47/48re transmissions. I always replace the solenoid along with the sensor if found faulty. They are easy to replace you just have to pull the pan off to replace.
3-Another thing it could be is a sticking valve in the valve body and the only way to repair it is to replace the valve body or have it rebuilt by a professional. I have special tools to clean up the bores and valves so they float freely.
4.Another thing you could check is to see if the output speed sensor is broken or loose on the driver rear of the transmission. It is normal for it to feel a little loose.
I hope this helps! It is hard for me to say for sure what is causing this because I have run into all those problems. Thankls, Richard