I would suggest you work with your builder to redesign the height for each level. As mentioned, BCA requires a minimum of 2.4m finished floor to ceiling height for any rooms so your 2.35m for mezzanine will not pass TOP inspection.
a 2.5 storey house can be built up to 12m in height. with your 5.7m plus 2.55m plus 2.75m, you have a total of 11m. add in 20cm for each floor slab (mezzanine, 2nd storey and attic) will be 11.6m. If your roof thickness is less than 40cm, you can actually allocate height to the 2nd storey.
Also if you are planning to do false ceilings to hide the beams and such, you will lose more height as well. The problem with low ceiling is that heat gets trapped within the rooms. For your inter-terrace, you have no side windows as well to allow for the heat to escape unless you are going to do set back on the sides to carve out space for side windows. Another potential issue with low ceilings is that if you plan to install ceiling fans, the low height will become a bit dangerous. a DC ceiling fan will have an overall height of about 35cm. So if your ceiling is only at 2.4m, it means the fan will be only about 2m from the floor and can easily be touched when an adult raise the arm upwards. If you have small kids, they may jump off the bed and hit the fan as well which is very dangerous.
While it looks and feels grand to have a double volume ceiling, you also need to think of the practical aspects of living in the rooms upstairs with such low ceilings. If i'm not wrong, newer flats are now designed with floor to ceiling of about 2.6m so your 2.55m is actually lower. The 2 videos you shown are houses which are in 3 storey zones so they have more height to play around with to create such high double volume ceilings. Unfortunately you don't have that additional 3.5m in height to play around with for your house in a 2 storey zone.
If you can, reduce the height of your 1st storey by a bit and add that to the 2nd storey instead.
Just to share, my house is also in a 2.5 storey zone and it is also designed with a mezzanine. the floor to floor levels split are 2.8m (1st to mezzanine), 2,7m (mezzanine to 2nd), 3m (2nd to attic), 3.5m (attic to roof). But my architect done a good job with space planning and allowing for drops for certain areas on the 1st storey so the result is that that one doesn't feel the low height levels. I also have a double volume ceiling is is about 5m high. I installed ducted aircon as I don't want to have the wall mounted split units exposed.
Anyway, if your land size is about 2000 sqf, there is no way you can get such a big build up area (1677) for your 2nd storey. Assuming your land dimensions are 20ft wide by 100ft deep to give you 2000sqf, this will translate to a dimension of 6.096m wide by 30.48m deep. URA standard setback for landed houses is 7.5m front and 2m back. So with this setback in mind, your house foot print can only have a max of 6.096m wide by 20.98m deep which gives an area of 127.89sqm or 1376.6sqf. Of cos I'm calculating based on standard planning norms so if your house is in an area with slightly different planning criteria then my calculation will be wrong. But the main thing is that you need to check with your builder on the exact dimensions of each room you want to have aircon in so you can do the planning correctly. Else you will be wasting money in over-sizing the aircon requirements than what is really required.