Sorry, I missunderstood the comments and/or techniques. But if someone wants to cut housings with a router, the festool jig with the sliding table works great to get an accurate housing with a flat bottom.

To clarify, bottom of image bears on housing.
I would pare out the shoulder colored in orange on both sides of the tenon, prior to labeling and end sealing.

And, I used a router extensively for fully housed timbers.
No sneezing, I wore a cloth mask I picked up a few years ago made out of some sort of filter material.

But, cleaning out the dust was always a chore.

Ok, that makes more sense than reworking the housing. It's just a way to more likely ensure if the housed member crowns with a check, the outside edges maintain the contact without the crown pushing the whole joint apart, right?

Apparently, I'm better looking with a mask anyway. And no one can see me talking to myself

yes, and to allow a tight fit on raising day. that little bit of extra wood removed isn't doing anything, and end grain isn't going to get any longer.

From a hand tool perspective the housing is where the excess is removed. I don't spend any time trying to make the housing just right, usually guess at the scoop and when I check it with a straight edge it is grand. I sure don't want it high.

BTF, how old it your oldest frame and have you been back to see how tight the joinery is holding? I see gaps on certain joints, most likely related to species and twist, spruce is usually the worst offender.

First frame was 5 yrs ago. Its all still pretty good. Just had some opening on the heel of the unhoused kneebraces where it shrank across the grain. I house them now too. I am using dry df and drawboring. Point taken though with the possible problems of shrinking timbers. Anyway, the festool router jig works great. I use the slider that you can get with it freehand. I put some uhd plastic tape on the stainless steel slider to keep it from damaging the aluminum jig. Just have to put a template guide on the router. I recently switched to a 3/4" insert bit with replaceable knives. It's easier to keep a bunch of sharp disposable knives.

After re-reading this thread, and thinking about the scooping technique, I have modified the housings I do. With the new 3/4" insert bit I'm using, it is not difficult. The router is being used with a 30mm template guide, which leaves a good 1/4" border around the housing template I am using. I can easily cut the housing 1/8" deeper except for the last outside 1/4" which would be as acurate as possible. This would be similar to your scooping done with your hand tools and hopefully have a similar effect. I think.
As far as gaps from shrinking, I was lucky enough before doing any traditional timber joinery, to get the best advice from a local old german timber framer. He used to cut the timber hybrid components in the Mcmansions ( I hate that term, because there are some really well built homes) I was framing. He told me to make sure what I used was really dry. It seams though that that can be easier said than done, especially given a person's location and local species. I.suppose

Darn phone.... I suppose that is why these (your) techniques are important to share. An ounce of prevention so to speak