Nope, Critic - the engine IS in fact the 3.5L dohc ISUZU engine! The Passports (Honda) are in fact all Isuzu as well; with the exception of the automatics being GM 4L30-E.
Any transmission issues you can blame generally towards owners not doing frequent enough service intervals, as well as GM's overall not so good design; though I can't complain one bit about the two automatic rodeo's I've had. Both have gone well over 150k miles on original engine & transmissions with rough lives.
But, I am the original owner of both.
The 3.5L engine is in fact all Isuzu that *can* be prone, just as any all aluminum engine to headgasket failures if the owner has not maintained the cooling system, and/or choses to use a non-Isuzu thermostat and doesn't change it frequently enough.
The 3.5L dohc's are NO MORE a risk for headgasket issues then anything else on the street.
The Rodeo's - as a general, do not have the 3.5L engine, there were in fact only a very few of them made in the 2004 model year and they are labeled as Direct Injection engines.
The 3.5L engine IS the norm in Troopers from the 98-2002 model years; the 98-2001's WERE in fact prone to being oil burners and some owners were not aware of this until it was too late and rods were thrown - THIS was a defect in the design, with some owner neglect being of issue as well.
The 98-99 Rodeo years with the 3.2L dohc DO have the tendency of cracked head at the #1 cylinder - again, a defect.
Isuzu's didn't come to have many issues until GM got more involved - this is my personal feeling.
Again, I've had 2 Rodeo's, a '91 & '97 (which I currently still own), and they've both had less work than any other vehicle I've ever owned.
I have NEVER had a single cooling, transmission, or electrical issue; unlike some dodge and ford vehicles within our close proximity right now.
Important things - flush that radiator, put in a new Isuzu thermostat (if it's not been done recently), timing belt (if it's original, may come due in the next year - otherwise, the belt is typically good for 100k.
If you do NOT know the history of the transmission, do a few partial fluid changes, including dropping the pan and changing the filter. The Axiom probably has the dipstickless transmission same as my Rodeo, in which there is a special fill procedure to follow.
Again, thank GM for that design.
Visit some Isuzu forum some time, most of these vehicles far surpass other makes and models on original engines/transmissions; many of the ones you see broken down are from owners neglect - which can be said about many other makes/models as well.