Complicated.
Does your wife have a PPS number?
If not, can she get one?
If she has a PPS number, can she get sickness/health insurance to cover her whole family, including her spouse? If so, would that help?
It is advisable when contacting state offices re getting PPS number or any matter to phone first and to follow up with an e-mail, as the decision is only valid when received in writing. So e-mail
info@welfare.ie to ask your question in writing, and to get answer in writing. The same with Garda immigration - e-mail and explain the position, and get a decision in writing.
It would not be advisable to mention that you are working at present when talking to any of the above offices, there appears to be doubt as to your right to work, so this could cause trouble. Obviously don't lie if asked, but don't volunteer the information either.