the 5R110 (aka Torqshift) is a 5spd auto. the "6th" you mentioned is the RPM drop of the torque converter locking up (direct drive, 1:1). a constant lock/unlock of the torque converter is a sure sign of converter issues. you can try a flush and refill, but it will either prolong the inevitable or cause it to crap out completely.
The 5R110 is a 6 speed that only uses 5. How? It can use OD in 1st, 2nd, AND 3rd. A more realistic representation of how a 5R100 shifts would be:
However, because 4th is 1.09 and 5th is 1:1, it shifts from 3rd to 5th. Thus making the shift pattern 1,2,3,5,6 TC lock. If you are basing your claim from an Edge monitor of gear indication, know this, Edge is counting the "shifting events" NOT the actual gear. The ONLY time a 5R110 uses 4th gear is when it is below 10*, even then it only shifts 4 times: 1,2,3,4,6. I know most websites show 4th as 1:1 and 5th as 0.71, but that isn't true.
While I don't have the references, it's out there. I used to use Edge and thought that the 5R110 was strictly a 5 speed. The transmission settings on your SCT call for (among the other shifts) "3-5 shift pressure" and "4-6 shift pressure". Look up 3-5 Shift Flare in this forum or on Google, it is exactly what I am talking about.
One last thought to throw out there, TCI is selling a 6-speed variant of GM's 4 speed 480LE. Do you know how they did it? It's an electronically shifted transmission and they reprogrammed it to shift like a TorqueShift. Simply, they use OD in ALL gears, not just HI gear.
Click here, scroll down to the transmission part. http://www.intellidog.com/dieselmann/60psd.htm
See page 38 on this PDF link also. http://www.fordtechservice.dealercon.../Dobdsm304.pdf