You might just have to sacrifice a level to achieve the desired attribute scores. Since I tested and it didn't always stop at the part where your character is ready to level up. Although I don't know exactly when do the attribute bonus stop adding after you've reached the level up stage. The character's leveling was supposed to be flawed. Otherwise, you'll have to rely on the ingame bonuses that you can find every now and then, it's how the game was designed.
Once you've hit the level up sequence, you can continue advancing your major skills which will result in an immediate level up afterwards, however I believe that during that next level up you can force a +5 on every Strength and Endurance. There's always a chance that you won't have a +5 on any attribute, which isn't necessarily bad. My highest attributes are speed and agility.
While on my end I can't really complain, because I got a Wood Elf Pilgrim with the Shadow.
You don't necessarily need to exclude those skills from your majors if you wish to improve your attribute.
