I would look at three things.
1. Your shift cables, when you tilt it up is the tilting causing any pull or push in addition that is allowing it to shift free?
2. The shift linkage just above the lower unit. Make sure the two nuts are tight together, if not, adjust until you can shift free. Honestly, this is where you will probably need to make the adjustment even if it is the cables, given the change in tilt is minimal. If its significant you would need to adjust the cables.
3. Lastly and hopefully not it, would be the dog clutch teeth being rounded. I don't think it would be this since you can tilt and shift freely.
Good Luck,
Eric