Has anyone heard of a model similar to a random forest which fits a linear regression model in its leaf nodes?
M5P Model Trees are the closest thing that I'm aware of.  In these trees, the leaf nodes are linear models.  The difference is that the leaf nodes learn a multi-dimensional linear model instead of single-dimensional.
(If you had a single-dimensional model at the leaf, how would you know which feature to use in the regression?  What is the advantage over multi-dimensional?)
Of course a model tree is just a single tree, not a forest.  But you could easily build a random forest composed of model trees.