You can use any standard waste and overflow (W&O) trap assembly…you just have to fit it into your construction. or, if you don’t want to use a manufactured W&O, you can plumb your own, so long as your plumbing is up to code. BTW, code does require you have an overflow drain…
This topic is very interesting to me as a plumber, but I’ve got to say it seems to be straying into strange territory. I’m not sure it’s very useful to most of the questioners here. It’s no secret here that I’m a Yank liberal plumber and support the DIY activism of homeowners to learn about plumbing and perform responsible work on their systems. One of the things that allows DIYers to do so is the availability of relatively easy to use standardized fixtures, fittings, and pipes. The other thing, at least in the USA, is that most jurisdictions allow owners to do their own work if they apply for a building permit and can present approvable plans and pass final inspection.
The problem with the “custom” type of installation we are discussing here is that it requires a very high level of plumbing expertise, not to mention other specialized skills like carpentry framing, plastering, and tile-setting.
It COULD be done by a really competent DIYer. The fact is that many otherwise competent licensed plumbers would have a rough time building such a tub, and even fewer building inspectors would be able to pass proper judgement on their work. That’s all I’ve got to say about it for now.