I thought the problem is only if you were auto-running at your old speed. If you're not on auto-run, and just keeping the joystick/direction key pressed for movement, the change in movement speed should kick in after a delay of about a second or two. I could've sworn I've seen this happen with my NIN AF boots when the game goes from day to night.
This is correct.
Autorun >> switch to movement + = staying at whatever autorun speed you were on in the first place.
Running or stopped >> switch to movement + = move at whatever enhanced speed.
This is true for all types of speed enhancements. Degradations, however, will have their effects showing immediately with 1 exception. If you're running with autorun and hit the button to walk, you will not immediately start walking. You will, however have a penalty applied toward turning your character. This is due to the fact that it takes less to turn a slower moving body the same degree or rotation.
If you are on auto-run and use flee: You'll run at normal speed till autorun is removed. Auto-run immediately after purchasing an outdoor chocobo: You'll ride the chicken at the same speed as people running beside you.
Regarding dreamland boots and stormsurge, I can attest to both working. Perhaps you had an odd piece of gear that didn't belong that would have offset the stormsurge bonus?
Regarding anything pre-75: Everyone else answered that job specific merits will only apply to that specific job when it is level 75. Any cap for whatever reason will deactivate the job specific merits.