If you do a search you will find a great many things NOT to do.
For jack *stands* I've seen a great many terminally stupid tricks, including cinderblocks and plywood (often combined

) The *good* solutions for crazy high stands seem to involve pipe and tripods.
However, for a jack proper, you *want* it to move (unlike stands which you very definitely do NOT want moving

) The trick there is to have it roll when you want it to, and stop when needed.
Plywood is tricky as a structural member, as each ply *will* crush, particularly if it's the cheap stuff (i.e. not A-grade or whatever it's called -- been YEARS since I've done woodworking) and has voids on the inner plys. What happens when there's a knot under the contact point to the jack? Once that ply crushes, there's more weight on the next one, and pretty soon you've got some compressed plywood.
Hate to say it, but when safety is involved, you gotta pay to play. $70 will get you a 3-ton jack with 20" lift at Harbor Freight; they also have a 2.5 ton long-frame that does 31" + (but it's $170, grrr.) [You'd also have to pay for the ride as it looks like the HF's in NM are three hours from you, which sucks. Roswell is BFE, isn't it?]
Sears lists a 19" lift one for $72, but they don't actually seem to have it.
$90 gets you 20" at Kragen, and both stores in town say that have it. (How I love the Internet... I never have to call pimply-faced eighteen-year-old idiots at parts store counters!)
http://www.partsamerica.com/ProductDetail.aspx?MfrCode=PNE&MfrPartNumber=280038&CategoryCode=3397
Your current jack may have a screw assembly on the cup so that it lefts up some ... but you're right, putting anything on the top is asking for trouble. Even with a welder, *I* wouldn't do anything to the top, 'cuz would increase the leverage on the center, which is a weak point.
There are some ~15" lift units available, but when it comes to safety, I like overkill. I finally killed the first floor jack I bought (a Craftsman) after about ten years ... with a stunt that involved dragging the crewcab sideways. I got a slightly more upscale one, also a Craftsman, as a replacement, and if I'm nicer to this one, I figure I've got a couple of decades yet to go.
-- A