Hi Tim, hope your Wife has a sense of humor
Extruded has a lower molecular weight and absorbs solvent cements faster than cast or cell cast acrylic. Solvent cementing the two can result in joint failures and crazing due to different material expansion and penetration rates of the solvent between them. Extruded tends to store more internal tension (used to work with a guy like this) :hilarious due to the way its manufactured, frequently rolled or squeezed into shape. (its also more uniform in thickness).
When the two materials become liquid in the solvent medium and weld together the difference is undetectable until the solvent starts to evaporate. Because of the different expansion rates between them, internal stresses within the joint can occur. This tension can stress the joint and induce a failure or cause crazing. It may not even be visible until the tank is filled and under pressure.
Unless annealed, acrylic tanks should be seasoned for several months by sitting empty before filling with water. This it to allow the material time to relax before the pressure/tension of water is applied. This process is for cast acrylic.
You could bond the two with #40 if the machining is good but IMO the weld would not be as strong as one produced by using #4 with the same type of material. I would recommend using straight cast or cell cast acrylic. Ive seen extruded used for skimmers though. You could practice by making a couple smaller QT tanks, and since your a good woodworker many of the same skills will transfer over, especially with a router.