If there is a supporting wall below, somewhere near the middle, you can join or butt the timbers over that - it wouldn't be a problem structurally at that position.
You can stop the strengthening pieces some distance short of the ends because the bending stress is at a maximum at the centre of the span, and tails off to zero at the supports. The remaining (unstrengthened) joists at the eaves will be sufficient to take the lower bending stress in that area.
You can stop the strengthening pieces some distance short of the ends because the bending stress is at a maximum at the centre of the span, and tails off to zero at the supports. The remaining (unstrengthened) joists at the eaves will be sufficient to take the lower bending stress in that area.