Mr. Morningstar, you have surfaced. How is the new piece of land and work scene going?

You do ask a good question there Michael. I'm pretty sure I understand your question, but it's not utterly clear to me, so if I go off on the wrong tangent, let me know.

You question relates to how to fit hari to round keta. One point: taiko is the name for one type of treatment ("naguri") of hari, and refers specifically to hari that have had their sides slabbed off and the rest left in the round. It's also called "taiko-otoshi". Other treatments include hachi-men-tori (eight-face faceting), chouna-men (adze-dubbed face), uri-kawa-kiri ("melon-skin cut"), etc.
Now, the keta need to be of deep enough section to receive the hari when the drop-down dovetail connection is used. Typically, after the hari is connected, the amount of relish left on the face of the keta below the lower surface of the hari is 1/3 to 1/2 of the total height of the face.
It is a fact that these connections on round keta are going to be weaker than on square beams as there isn't as much meat there for the dovetail. It would be MUCH better to lap them with a cog joint of some type wherever possible. In either case, it is a joint that needs reinforcing with some metal. A better choice is to use rectilinear-section keta with log hari, but I appreciate you may with the all-log look for some reason. The beauty of logs is their strength in the round, and it doesn't make so much sense to compromise that by hacking deep housings into them.
When using round keta, and drop-down dovetails on the hari, you must try to keep the depth to the 1/2 mark, possibly a smidgeon over, otherwise you run into difficulties, as you noted, as the lower face of the keta continues around. It is possible to fit the hari lower down, even to parallel with the keta, but you may not be be able to use the drop-down dovetail (complicating assembly), or you will be taking so much meat out of the keta to provide adequate housing depth that is ends up weakend excessively. In cases without a post underneath, or some other form of support (like a cantilever above that is connected) the strength of the connection would be worsened - you want maximum possible amount of fiber of the hari supported, without leaving too little relish on the keta below it. Since the end of the hari is faceted to give flat bearing surfaces, you can drop it slightly lower than the theoretical 1/2 way mark.
The treatment of fitting to the same height is seen in the keta to keta connection under a hip on a veranda, with that funky keyway joint, but that's about it. If the butt of the hari is flared a lot so that it would be tough to keep it to the 1/2 way insertion mark, then the flare must be removed, but not so much that you end up weakening the hari excessively - and I know you know that so I won't elaborate further.
Getting back to the keta to hari layout - how to achieve the correct depth on the keta housing: you can establish the to centerline and the lower centerline on the keta quite readily. The keta can then be rolled on its side so that the top-bottom line axis is horizontal. Then, at each housing location, you need to be sure that the log is supported by something that is also level to this axis. You need to ensure that the log is not forced out of shape by being laid on it's side as well, by checking your top/bottom layour lines with a string line. with the log on its side, and a level reference surface underneath, it is a matter of measuring up plumb (you can use a pair of sashigane from your top and bottom lines to the housing depth you want. Then it is a matter of cutting down to the lines. With a pair of sashigane you can also confirm whether the housing is in plane with level or not.
Depending upon the shape of the log used, the housing can be kept uniform in relation to the top/bottom line reference axis, or you could vary the depth, making sure that you remember to adjust each keta housing to its hari as required.
And you could rig up a box to do the same cut out with the housing router mounted on it, or a regular router quite easily too. The box could be made to index against the top/bottom layout lines.
You also need to mark out the mizu-zumi line on both the keta and hari so that you can be sure you are bringing the hari down to the right depth. That line can be laid up off your reference surfaces too. On the hari, the mizu-zumi must be judged carefully in relation to the shape of the end of the log and how it will fit to the keta. On the hari the mizu-zumi is the primary reference line.
As far as the rest of you question, regarding determining the depths of dovetail, etc, it seems to me that once you have a reference face, all of the other depths you need are determined from that.
The issue with using logs for keta is that you must choose the hari carefully as there is less flexibility in terms of housing depth available for the hari. There is a narrower range of logs that would fit well to the keta. While deeping the housing makes for a wider face on the keta, it also weakens it, so you have less room to play with.

Anyway, I hope that answered your question. If not, let me know what areas you need me to focus on, and I'll do so.

Chris


My blog on carpentry practice, East and West:

https://thecarpentryway.blog