There is an excellent article in one of the older issues of Autoharp Quarterly (Volume VII, Number 1) called "When It Hurts to Play", written by Catherine W. Birtell, MD. It is repeated in the Mel Bay publication, "The Autoharp Owners Manual" (pgs 98-101), compiled by Mary Lou Orthey (MB99361 - $19.95 US) which is an excellent all purpose resource for the 'harp player.
I have some quarrel with Bryan's arrangement and use a Majors forward, 7ths in the second row set tight to the subdominants, and minors to the rear, arrangement. The problem is that Bryan's cradle keeps the harp flat across the chest which in my case would prevent "throwing the harp", a technique of getting tremelo and phase effects by quickly shouldering the 'harp off towards the mike and using your right wrist to pull it back as you continue to play (a good technique if you need to provide a Celtic style drone to hammered dulcimers).
(And yes, I do have some suspicion that some twit will comment on "throwing the harp", but we all have to deal with someones "special child" at some point in our adult lives.)
By canting the harp around back towards your left and reaching around the 'harp a bit more with your right hand to play the strings, you can reduce the angle on both the wrist and fingers of your left hand. Yes, you increase the angle on your right hand, but since it is moving in many directions at once, while strumming and picking the strings, it is not as likely to cramp up.
As the others have indicated, you should let the pain subside before trying this. But once you feel up to it, you might want to lose the strap arrangement, sit down, place the 'harp in your lap and tilt it in a manner that makes sense to you (and your left hand) and make up the difference in the angle with your right hand. If you develop problems with either hand at this point, you may want to consider the suggestions of playing it Kirby Snow style, in your lap.
Incidently, I stopped by the the Mt. Laurel Autoharp Fest in Newport, PA this past weekend and it was the most bang for the buck I've had at any festival including Augusta, Common Ground etc. Autoharps ain't what they used to be, with split/and composite chord bars doing floating pentatonics. Watching Karla Armstrong do N. Coles "When I Fall in Love" with all the blues chords on an ultrasonic 'harp was stunning and left the 'harp crowd with wet eyes and the rest of the crowd with wet seats.
Alan Mager finally won the championship, and this, with four days of classes with the best for $65, was a true bargain. Food was provided by a local Grange and I had a great meal every night for around 5 bucks. I highly recommend that if you're past the Church Lady phase of autoharping and want to see the future while Europe sleeps, save out the latter part of June, first of July weekend next year for this one. It's more fun than white people oughta have. Good Luck!