Hi,
One advantage of the big coil of PEX as the heat exchanger is that the PEX coil itself holds about 10 gallons of water. Since most hot water demands are less than 10 gallons, and the 10 gallons in the coil is already heated up to full storage tank temp, its a 100% efficient heat exchanger most of the time. After the first 10 gallons, its still pretty good because while PEX is much less conductive than copper, it has much more surface area.
The system in the link you gave is my system, and while I have no issues at all with copper heat exchangers, I have to say I'm really pleased with the performance of the big coil of PEX.
If you used the crawl space and allowed 2 inches below and 2 inches above for insulation, you have about 18 inches left -- enough for a big coil of PEX, but you would have to build the tank around it. The 22 inch crawl space does not sound like a lot of fun to work in, but if it allowed a simple drain back system it might be worth it.
These kinds of EPDM lined tanks can also be built in in cylindrical shape out of a single piece of sheet metal wrapped in a circle -- like the tanks that STSS sells. This might be easier to work with in such a limited space.
Some of the other people who have built the $1K solar water heating systems have use other approaches --
Solar Water Heating Projects and Plans
Mostly with copper, but some mixed systems.
I think that Chad's system has a tall skinny tank that might fit your space.
Gary