Nice looking rig.
I installed an '05 H27A in my '93 Tracker, and had not heard of an immobilizer. I was long time getting all the wiring blended into my Tracker wiring, but working fine now. My biggest problem was I missed a ground wire on the BCM so it kept throwing a communication code. On both the '03 and '05 models they use a CANBUS (for communication between comuters) and you need the three main computers ECM, TCM, & BCM to be running or it will throw a communication code; In US that prevents both 5th gear and torque converter lockup, along with samller transmission programing changes. I got my motor and trans. with just the ECM, and it would mostly work but had the communication issues I mentioned.
How many computers are you running?
As I have not seen wiring diagrams with an Immobilizer, not sure what it takes to satisfy it, but should be doable.