Here is the link to Putnam's web site:
http://www.putnamhitch.com/MainPage2.htm
I may be a little dense since I don't quite understand your question. You stated that you need to get a hitch "installed" on your 2002 Tundra by next Tuesday but the shop can't get the Draw Tite model in time. Do you already have a "Receiver type" of hitch installed on your truck? A receiver type of hitch for your vehicle can be installed by a lot of shops, including Pep Boys, Sears Roebuck, etc. Most of these shops will stock a wide enough variety of receiver hitches to fit just about all vehicles, and, the installation just takes a few hours. Installation of a receiver hitch will provide your vehicle with a square socket that will take a 2" x 2" hitch bar with a ball. How far the ball should be mounted above or below the level of the bar itself will depend on the height of your trailer's hitch with respect to that of your vehicle's receiver hitch. For this reason I personally would not have a shop fabricate a 2" x 2" hitch bar for a weight distributing hitch (WDH) without having the trailer on hand or available so that these dimensions can be obtained.
You might wind up with the situation that my wife and I had. We owned a Reese WDH that we used with a previous travel trailer. We took it with us on the 900 mile trip to an RV dealership to pick up a used TM that we agreed to purchase. When we arrived there, the ball on our old hitch bar was too low to allow our truck to be hitched to the TM. We therefore purchased from the dealer an offset hitch bar (about $25 swan-necked or S-shaped bar) with the ball mounted at a higher level. This allowed us to hitch our truck to the TM. We couldn't, of course, use the WDH for the return trip home. It worked out okay as a temporary measure - temporary I say, during our leisurely week's towing along the coast of Oregon and California to reach our home. When we got home, I cut our old Reese hitch bar apart, mounted the ball higher up and welded it together. The photo shows what our old hitch bar looks like after I modified it.
My point is that I feel you should get the trailer first, then obtain a hitch bar (stock or modified) that will allow you to hook it up satisfactorily to your truck. It may save you some grief. Your dealer might suggest that you buy an adjustable hitch bar. You may discover later that your adjustable hitch bar doesn't have sufficient height range to allow your truck to be hooked up properly to your trailer.