Seat

The seat frame is determined by what cover you want to use. Mesh nylon is cheap. Grommets are more expensive then the nylon in fact.

Round or square, it doesn't matter a lot for comfort as long the seat isn't very narrow. If you decide on square, put an old road bike tube round the bottom frame to create a soft edge for the seat fabric.

Another cover could be one made with a long ribbon diagonal on the seat or in a woven pattern like a wickers basket.

Some may want a hardshell. In this case it will not give extra support to the cross-t. Remember those small diagonal stabilizer strips? Make two of them for extra strength and the seat can be on the main tube only.

to be continued.