Shift on the fly is an ad campaign made up by marketing folks. There is a ton of stuff to spin up (unless you have a late second gen without the CAD on the front axle). I've had my T-case apart and I WILL NOT shift it above 10-15 mph.
If you are familiar with manual transmissions, the T-case uses a nice synchro ring to spin up the big, thick gear that is on the rear output shaft (weighs a couple pounds) which spins the chain (a few more pounds) which spins the output shaft gear (weighs a few pounds) which spins the DRIVESHAFT which spins the FRONT CARRIER. Lots of mass to accelerate with a synchro ring. Oh, and the shifter fork has plastic wear pads on it where it rides on the shift collar.
As for your problem, make sure the T-case is full and the fluid is in good shape. When you shift, be going slow with you foot off the throttle (auto) or in neutral with the clutch in (stick). If it still doesn't want to go, stop and put the trans in neutral (not park). For shifting into 4 Lo, stop and use park (auto) or in gear with the clutch in (stick).
The backing up 15 feet was to disengage lockouts, it doesn't do anything on these.