The "I have small hands" idea
Instruments- discuss specific features, luthiers, instrument problems & questions
This was from a page about reach in piano playing ( http://www.pianoworld.com/forum/ubbthreads.php/topics/1900021.html) , but, just substitute 'dulcimer' for 'piano' and 'keyboard' and I think, it could apply here too - as an approach to the whole thing ... although, as Lisa says, you need to factor in arching the fingers...
Start with the shoulders and make sure they are tension free, then the elbows, relax on down the arms, limp wrist will drop down from the end of your arm, fingers will spread loosely to create a natural curve. It's a feeling like you have no bones!
Then whatever music you are playing lift your forearms up without lifting your shoulders, drop onto the keyboard and start the music playing.
updated by @anne-bowman: 07/27/16 03:57:35AM
Check several times during your practice to see if your shoulders are up around your ears. You will notice a lot about yourself if you make yourself the subject to notice instead of the focus on the music. Play something you know to check this out. Start and stop without producing tension - What did you catch yourself doing?
And, I wouldn't force any additional movement into the webs of the fingers except to maybe gently place the opposite hand between each of the four webs per hand and moving gently to the bottom of the web and "rocking" between the expanded web minimally.
Then I think splaying the webs apart without forcing by sitting on the bench at the piano with your hands parallel to your knees in curved hand position no tension. Again, just a bit of slow opening of the webs 3 - 5 times all at once without splaying the finger tips . You will feel the reaction in your fore arms and I think it causes a very unpleasant feeling on the outside of the forearm. This is just to make the webs flexible should you need expansion between fingers for wider intervals. Don't be excessive in any movement.
Comforting hands by a little massage after a workout is easier to do with a little lotion. I sometimes say aloud "Good hands, nice hands" when I'm amazed at what they were able to do.