Nah my Mark2 was factory 2JZ-GE, just replaced the engine when it blew the head gasket.
Get a UCF10/20 celsior as a tow vehicle... pimpin luxury and 4.0l v8 up to the task... upgrade the brakes and whack a blower on it
But seriously, theres a reason almost everyone uses either a commonwhore or falcunt if not an SUV to tow their race cars... I know Toyota reliability and build quality is preferable, but I'd rather trash an oz built car than ruin a good Toyota if you're going to tow with a monocoque chassis.
Most of my car transporting I did with a 93 diesel Ford Courier single cab LWB. Slow as shit but stable and capable. If you have the funds, just go newer model with turbo diesel and it'll be a good vehicle. Then you can add airbags and french the number plate
As you're towing an AE85 you might be able to get away with a single axle trailer, reducing the towed weight and allowing you to get away with something like Celsior/Mark2, but a tandem will be more stable and better in the long run.
tl;dr
Cheap option - Single axle trailer with Falcon tow car
Better option - Tandem axle trailer with SUV/Turbo diesel ute
Rumple dee pumple dee doo...