I use a 26 inch no-name (but quite decent quality) rip saw purchased from a car boot sale for £1. Of course, I had to learn to sharpen it ...
Plane one face flat, then run a marking gauge round using the planed face as your reference. For final thickness you will want around 2mm, so mark at 4mm to allow for cleaning up.
Groove that marked line to about 3mm depth, I use a tenon saw.
Place your wood in the vice so you can cut at about a 45 degree angle, keeping the saw blade horizontal. If you put much pressure on the blade the cut will become more ragged internally (or at least, that's my experience). Every couple of inches of cut, flip the wood so that you're cutting from the other side.
When you get down to the vice, you have to improvise!
Once your first slice is off, plane flat the face of the timber and repeat for the second slice. Your book match is the faces of your first saw cut.
This is fairly slow work because you need to go gently. I'd cut your timber to a little over final dimensions before resawing, as a 6.5 inch width board is substantially more work than a 5.5 inch one.
I have done this with an ordinary hard point panel saw. It goes a bit slower, and the cut is even rougher, but it's quite achievable.
My saw cuts are always cleanest at the start, and then get more ragged towards the end of the cut as I lose patience and put more elbow into the sawing.