Michael,

please excuse the delay in responding, I simply forgot.

The alternative engeta joints I've seen are simplified versions, ofter with a stub tenon, detachable nose, and all-thread to pull it all together.

Fitting multiple hari together can be done in a variety of patterns. It depends upon what sort of logs you have - in terms of their shape. If using taiko, then there is a mizu-zumi (water-line) established on the flat sides, which is used as a reference. Otherwise, you are scribing, one by one. Lay a transverse hari - or several going in the same orientation, depending upon the pattern you desire - lay it out, do the cut it out and then fit it. Then take the hari that is to fit crosswise on top of it, orient it to plumb, and scribe it using the hikari-ita. The crossing points for the hari-to-hari are usually a form of cogged partial lap joint. With taiko, it is a pretty straightforward procedure to transfer layout marks; with round or multi-faceted logs you will be scribing, plain and simple.

I hope that answers your question well enough. Personally, I quite like the idea of 'weaving' the hari; say one across the short span, then one crosswise on top spanning the long axis of the building, then another crosswise on top of that on the short axis. You need particular shapes of hari for that, ones that do not have a consistent bow, rather an accelerating curve or a curve concentrated on one end of the log, or a wiggly log.

Chris