This approach won’t work. The PIC17 is a very different chip, it especially has only an OTP (one-time programmable) memory instead of flash. Therefore it will be dangerous to program it with a cheap PIC burner, if this has never been tested before. With bad luck you will quickly loose two or three PICs and a lot of money.
In addition, the MIOS bootloader is located at a special memory range which is probably overlapped by the firmware. And it would require a special adaption for the PIC17 derivative…
Unfortunately my PICstart kit (which can burn PIC17 chips) doesn’t work on my PC anymore due to a missing COM port, otherwise I would be able to help you