It is possible your old converter was hurt/worn out, and that was causing it to slip too much to lock with a stock TCM tune. With the new converter, you probably want a trans tune to move the lockup apply & release points around to take advantage of it.
I run a high-stall converter, and it drove like ass on a stock TCM tune. With a good TCM tune, it is a joy to drive. Hit the throttle, RPMs come up to 3000-3500 for a second, truck instantly lights the turbo and starts pulling hard, it commands lockup after I pick up some MPH, pulls RPMs down to ~2600 and stays locked up from there through the gears.
You will be much happier with the truck once you have the TCM commanding lockup at part throttle. I have mine lock up at 55 MPH when I am below 1/3 throttle. I've played with locking it up in 3rd/4th, but it makes the truck too twitchy in town for my tastes, so I only do that in tow/haul mode.
If you want, I can post up my trans tune so you can see what I've done. It's a 5 speed, but you can copy those values and make up something similar for 5-6 and 6-5 and see what you think. Heck, just disable 6th if you just want a quick test. I run a 71mm turbo and a stupid cam, so I rarely let the truck drop below 2000 RPM if I'm touching the throttle at all. Might be a bit more extreme that you need/want. And tow/haul mode needs a lot of work, so ignore that for now. Let me know and I can post the tune if you want to look at it.