In addition, we don't know where to get a jack to
lift the beam the 1/4".

Any auto parts/hardware/box store will have bottle jacks rated 20 ton or so for
maybe $30. To lift easily you need something solid underneath, like some pieces
of 8 x 8" timber. Since the original installation of your joists was level, the
correction is not likely to cause any damage. No frame house is a monolthic
structure, and yours has merely settled over the years. Do what you feel is
best and good luck.

Joe