This was a disaster this morning; burned on the bottom and uncooked in the center. I sifted, etc. and am perplexed. Could the amount of flour be incorrect? I thought maybe the rhubarb should come in after the cream so they remain fairly large, too.
Are you channeling your best self with this comment? (If you're not sure, check out our Code of Conduct.)
It sounds like your oven was too hot, and perhaps the heating element was still engaged in doing its business whilst the scones were trying to bake? Was the rack in the center? Always wait until the element clicks off before putting in the dough/batter/recipe/foodstuff. Also, if this has if this has happened to you before (and even if it hasn't) it is always good to have an in-oven thermometer to get know your oven's thermostat idiosyncrasies (should it have any).
A final thought, scone-&-biscut-mixing should always be kept to an absolute minimum, the cream is added last because it activates the leavening, and you want to mix as little as possible after you have done that.
It seems like a food processor might not be the way to go with this recipe. By hand might be better.
I always do scones and biscuits in the stand mixer, at least for cutting the butter (and skipping the sift). Adding the fruit & cream by hand is a good idea.