First, you should be able to get a full 28" draw from a 61" bamboo slat bow. Drawing to 28" from 24" should take your draw weight up around 20#-22# anyway.
You can increase the draw weight without even gluing anything to the bow, using a technique called "loose laminate" that was popular in China a thousand years ago. You'll want to get a 1/8" thick length of bamboo, oak or maple that is about as wide as the bow in the center and a couple inches shorter than the length from nock to nock.
Center the new lamination on the back of the bow and start lashing, on either side of the handle with something like the thin paracord you can get from Michaels, or other strong thin cord. Make about 5 loops and tie it off. Seal the lashings with superglue.
Repeat about every 5"-6" until you reach the ends of the new lamination.