Swapping to private allows you to stick to your gynae of choice each time and also stay in class A ward which I find is very impt, you could really need the space and privacy and only Class A allows hubs to stay in throughout. Also, agree to convert after major tests all done by 3rd/4mth. You will need to start researching which gynae you prefer to engage though, the popular ones might not be available during your edd..
I would say its the best to do at week 20 as the detailed scan is included in the package and the ogtt test plus the 6 consultations that will last you till you deliver so you only beed to account for the meds and additional test till you give birth.