The IRR counts as your 'dual flight with an instructor' in its own right
Absolutely right - and fortunately the CFI I deal with agrees - though there have been alarming incidences (there was a thread on here a month or so ago) of the 'dual flight' starting to become a test with specified content.
I can see the benefits of the IRR including IMC, actually, as if you were a bit late with or partialled the IRR one year, you would at least have another 13 months' IMC privileges to tide you over while you sorted out the problem.
Tim