Speedometer is stuck at 20 mph. Sometimes it moves and then gets stuck again. Is fixing this expensive?

get your gearbox looked at

sounds like the coil spring for the speedometer needle is bad. you can replace it or buy a new instrument cluster. Look at local salvage yards for cheaper price.

Well you know it does not have a speedo cable since you replaced the speed sensor in the transmission.
My guess would be a problem with the speedo or cluster.

sounds like speedometer cable is gone or the gears between the cable and transmission which makes the reduction for sppedometer if no cable on that year they have a sensor

the speedometer head could be the problem

Pretty common problem with these. Here's a guide to learn how to fix GM instrument clusters yourself, I used it to fix mine and it worked great.How to guide for Impala instrument cluster repair

the sensor on the gearbox needs replaced common problem with that age group. sensers are around 20-30 quid hope this helps?

Common issue with the 05 Mustang instrument clusters, it's caused by failing stepper motors on the cluster's circuit board. It can be repaired, check out this page for more on how to get it fixed - 05 mustang tachometer doesn't work

loose connections would not cause it to stay at 20 when your going zero. i think something is stuck and the needle isnt moving freely. sometimes the sticker that have the numbers on it can fall away from the cluster and rub on the needle that why sometimes when you apply pressure to the trip reset it will work. the needle and odometer are also connected so once you fix the needle the odometer will work again. i would take the cover off the cluster and move the needle with your finger and feel if it sticks any where. if it is the sticker just drop a little sper glue down there, move the neelde forward and hold it down till it drys. if nothing appears to be holding it i would blow a can of air in by center of the needle to get any debris out of there.

This happen to me too. Had to get it replaced under my exstended warrenty that cost me the $200 deductable but would of coast over $400 if this happened later.