I think you need to ask INZ this question.
I feel that normally, the suggestion would be that you should apply for partner-sponsored residence straight away, which may be processed before your current visa expires. If it gets near the expiry date, you could then lodge a partner-sponsored work visa application, and that would mean INZ could issue you with an interim visa to keep you legal while processing proceeds. Whether or not they will be agreeable to your 2-in-1 idea, I don't know.
If you get the go-ahead, be very careful to keep copies of all your partnership evidence. Your applications may end up being dealt with in different offices.