Hydronic slab heating is fairly straightforward to install and not that expensive compared with other forms of central heating. If you try to cool the slab, it becomes a lot more complicated. First up, cooling the slab does nothing to remove humidity from the air, which is a large part of what makes you feel hot. Second, you need some way of controlling the heat pump between heating and cooling mode. Usually we use mechanical thermostats which switch on when the house gets below the set temperature, but when you change to cooling mode it needs turn on when the indoor temperature is above the set temperature, so instead of a standard central heating thermostat you instead need an electronic temperature sensor. Anything is possible, but the short answer is that having a chilled slab will be more complicated and more expensive than an air conditioner, and less effective. You'll also need to find a contractor to design the system, and because it will be a custom design if you have any issues in the future you'll need to get the same person who installed it to come and fix it, which is a problem if they move, go on holiday, or close their business.

Judging by the plan, the photos and your comments it appears that too much heat is coming in from high light glazing (clerestory windows) into the lounge and dining areas. Both rooms will be cold in winter because the direct heat from these windows is not enough and not absorbed in an thermal mass and they do not have ground level windows or glazed doors facing north. The elevated floor means that it is cold under the house so heating in winter goes down as well as up. The roof would lack adequate insulation due to the period in which the house was built. The roof tiles probably have another 15 years maybe a bit more so it is costly to insulate from the top (i.e. taking roof tiles off adding insulation then putting roof tiles back in again. The colour of them is contributing a lot to the heat. So what to do. - add external shading device to the highlight glazing, maybe timber battens 40 x 40 at 20mm spacings. This will block direct sunlight within the shading season. That helps to reduce heat intact and see how you go. If that does not work then - add a rigid foam core board to the underside of the timber ceiling, e.g. Foilboard which is 20mm thick r 2, then install a 12mm plywood ceiling lining under this. That way you retain the timber rafter ceilings but also one that has a light coloured (hoop pine ply) timber in between. (Note this is costly) - big gains in heat loss is achieved with underfloor insulation. Try r3 bulk squeezed tightly between the floor joists. Then you can plan for the future with the following - change glass in windows and glazed doors to a low e glass - install insulation into the cavity of the external walls using a company called envirowall. - replace roof tiles with a light coloured metal roof, replace the existing roof battens with a 100 x 40 batten so that you can install a 100mm thick anticon insulation. All of the above costs money and if you don't do it then it costs money to burn energy to keep the living rooms between 21 to 27 degrees year round (what we consider comfortable) so if it tough to decide what to do or not. As an alternative For about 40k you could spend 30 of it on solar cells, and an awesome battery (Tesla powerwall 2) and buy some wall mounted ac units. But that would be kicking the can down the road. But sometimes you have no choice. Good luck

As for the clerestories, glass is a very, very poor insulator & doesn't block radiant heat (sunshine). So in winter you want to gain more heat from sunshine coming in the house than you lose through poorly insulated windows (clerestories lose a lot of heat, as it's warm near the ceiling). So you want your windows to be unshaded in winter. Unfortunately your roof design means your northern clerestories will be shaded, losing more heat than they gain. So I see no advantage having north facing clerestories with that roof design. As oklouise says, north facing clerestories are much better with a skillion roof, as they will receive winter sunshine. As for western windows. All western windows are a problem in summer (& won't receive as much sun in winter as northern windows). Clerestories will be shaded for much of the day, but will still receive sunshine in the late afternoon. So I wouldn't be including them. You obviously want some windows facing your western yard. But I'd be reducing them, shading them with a western covered alfresco & using low-e glass to reduce radiant heat transmission. Southern clerestories. These receive no sunshine in winter, & leak heat. So I wouldn't be having these either. Maybe a case of form over function. You want form to follow function (as is the case with north facing clerestories with a skillion roof in the below example).

Great stuff. I hope to hear from other similar projects.