in NZ the ATPL is not recognised as much as a degree
I dispute the Degree is recognised more in NZ, I have one and it has made no difference whatsoever, if you have one then something else will be found you do not have to meet the shifting goal post requirements.
Yes there are points attributed to it in the Air NZ hiring point system, but if you spent those years at Uni flying a plane instead I bet those hours would give you more points!
As for doing a Aviation related Degree as well, the term 'all your eggs in one basket' comes to mind, but this old chestnut has arisen before on the forums.
My suggestion would be to do a qualification or trade in something as far removed from aviation as you can for when you are made redundant or lose your medical.