Hello Althea....Just guesswork but there's a possibility that the Nurse M. Sheedy mentioned in the 1920's newspapers is Mary Sheedy. She's mentioned in the Nurses Register of 1927 as having qualified in 1925 in Riverton. And she's also mentioned in the Midwives Register of 1929 as having qualified as a mid-wife in 1928. Happy to shoot lo-res scans of the NZ Gazette to you if you want.
No mention of Matron Sheedy in the first ten years of the Register (1901-1910). Maybe she was out of the nursing profession by then. Or possibly the Register wasn't all that accurate in it's first few years.
And, for what it's worth, when I was researching the Sheehan family I ended up with half a dozen notices relating to various Sheedy's. I'm fairly sure nothing relates to Matron Sheedy but it's no problem to shoot those to you, if you want. More grist for the mill.
Regards
Beg