Comparing Schlage vs Kwikset lockset handedness

I have a side door on my garage with a matched set of Kwikset handle and deadbolt but they lock/unlock in different directions.  This is a right-handed door and opens inward, i.e., from the outside the hinges are on the right, and from the inside the handles/bolts are on the right.  The deadbolt works the way I expect, as the top of the key (from the outside) and/or the top of the handle (on the inside) moves the same direction as the bolt.  The key to the handle, however, works the opposite direction.

Handedness of door locks

This is the 'handedness' of the lock.  Rather than left or right, it's defined as clockwise or counter-clockwise.  The seemingly-correct 'handedness' for my locks -- from the inside -- is clockwise to lock, counter-clockwise to unlock.  But the handle's twist-latch turns counter-clockwise to lock.  I set out to reverse this.  And failed.

What I learned about lock handedness

I found some locksmith discussion web-sites where other people had asked about this.  There was a lot of confused replies as most people thought the original poster was an idiot who couldn't figure-out how to remove and reverse the inside/outside orientation.  Eventually I learned the following:

1. Some commercial locks are designed to have their handedness reversed but most residential locks are not.
2. When you flip a deadbolt from left-open to right-open, the handedness reverses too since the door-open action is the lock.  But when you reverse the direction on a handle the door-open mechanism reverses but not the internal locking mechanism.
3. Kwikset handles are all designed with a clockwise unlock. So in order for their handles and deadbolts to have the same handedness you need to use them on left-handed doors.
4. Schlage handles are the opposite, they're designed with a counter-clockwise unlock.  So their handles and deadbolts only match when used on right-handed doors.

Conclusions/Recommendations

I went to Home Depot and inspected the lockset displays.  I also asked the employees in that department but they were unaware of this issue.  They said people usually just accepted the mismatched handedness.  Maybe now they'll ask customers which way their doors open and use that as a means of recommending one brand over another:

left-handed doors = Kwikset
right-handed doors = Schlage