Leveling floor for laminate install

I'm trying to level a room in preparation for the installation of laminate flooring. The laminate flooring requires the subfloor to be flat to 1/10" over 4'. The room is 17' x 12' and the walls are supported by the foundation footing. There are two joists running parallel to the 17' wall that are 4' apart. The joists are 4" x 6" beams and the subfloor is 3/4" plywood.
The problem is the two joists are 1/4" lower than the walls. The 1/4" drop is constant along the majority of the room and reduces a bit as the joists approach the end of the room. The two joists are level with each-other.
We have considered the following options to level the floor:
1. Lay 1/4" hardibacker between the joists down the length of the room and screw them in place. Level remainder of the floors to the wall using quicklevel cement.
2. Raise the joists by adding a 1/4" shim at the top of the piers.
We are thinking of going with option 1 because we aren't comfortable performing option 2. We are worried we don't have the skills and we may cause damage. In addition, we don't know where to get a jack to lift the beam the 1/4".
Any suggestions on how to proceed with option 1? We ran a test run with the leveling compound with mixed results. The leveler doesn't appear be 1/4" thick (still drying).
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<< 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
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