If you only wish to be an instructor why even do CPL? It's no longer required, under EASA you can be paid as an instructor with PPL and CPL groundschool.
If you have your heart set on doing a CPL, do the ATPL groundschool then as you say you have 36 months from the last month you took an exam to get both CPL and IR. If you don't meet this requirement you will have to retake all of the exams.
You certainly don't need an IR, and at many airfields it would be no help at all unless you are flying suitably equipped aircraft and have approaches available. The main benefit is that you can fly "VFR on top" to teach simple lessons like straight and level, climbing, stalling etc which otherwise would not be possible with a lowish cloudbase, and still be able to get back down afterwards.
I instructed for two years before I did my IR, that was my original plan and it worked very well. By the time I did the IR I had around 1000 hours and it made the course so much easier.