I'm no flooring expert- but I am a very good carpenter (DIY'er) so I'll take a stab at this.
If I was faced with this job, assuming you have not yet intalled the new boards, I would use a Surface Planer to remove the excess thickness. You can remove thickness in approximately 1/32" at a time, or up to 1/16" in one pass.
If the new boards are finished in some way, or are nicely sanded on one side then it would be best to take the material off the backside of each board.
Most Big Box stores sell, or likey rent, surface planers. A decent Dewalt planer can be had for around $400 and is worth it if you have lots of boards to do. You can always sell it on Craiglist later.
http://www.lowes.com/pd_221857-70-DW734_0__?productId=1061487&Ntt=dewalt+surface+planer&pl=1¤tURL=%2Fpl__0__s%3FNtt%3Ddewalt%2Bsurface%2Bplaner&facetInfo=