Because you are not changing visa types you might not have to leave the country if you cancel the old visa, and get the new one on the same day, and it can be done. The WP is done in the country.
Lots of workers do exactly what you are planning. They'd apply for a single entry tourist visa, then extend it for 30 days. Now with the 60 day visa exempt entry it makes it easier, just needing the 30 day extension. I have friends that work 2 months on, and one month off, that have been doing it for decades.
the original plan was to include basic accident insurance with the bt300 fee, as a significant number of people leave without paying their hospital bills for injuries.
don't let people fool you. The immigration computer system is very advanced, and with your finger print, and facial recognition they know instantly who you are. They are also connected to interpol, and the FBI data alert system instantly. Ten years ago it was not so advanced, but now it is some of the best in the world, and constantly being updated, thanks to the US, and a few other countries.