A few seatpost comments. Lightweight seatposts may be butted, ie have thinner walls in the middle, alloy as well as carbon. That type of seat postis probably not an ideal choice when clamping a stoker handlebar. Carbon seatposts designed to be sturdy can be sturdy enough. About cheap Chinese seatposts - they are typically overbuilt and definitely does not have any wall thinning tricks, so I'd think that they hold up really well.

We've chosen to use high end alloy seat posts designed for mountain biking, without butting, the shannon hardcore seat post (the non-light version) which exist in several diameters and lengths, even up to 500mm.

Seat posts have minimum insert recommendation, and so have many frames. The frame minimum insert is not so easy to come by, can sometimes be found in the frame manufacturer's technical documentation. It's usually around 8-10cm. But obviously the heavier you are and the longer seat post extension you have, the more force is put on the seat tube / seat tube interface. The minimum insert has some margin, so a light rider with little extension can use a bit less insert.

Personally I like to have some margin though and like to be able to tighten down the stoker stem hard (to avoid slippage) without risking cracking the post, so I use sturdy long seat posts with lots of insert, especially since the tandem frame we have is really low making seatpost extension rather long (like on a MTB).