the timeout accumulates, so that after quickly changing channel up, then down, say, with timeout 15s, the info bar is shown for ~30s
I am unable to reproduce that, neither on HD-FOX nor HDR-FOX. If you changed changed channel again after 14s, the info bar would be on-screen for 29s anyway. The OSD remains for the set timeout after the last operation.
invoking the info bar with Info starts the fixed 30s timeout; switching to the previous channel with Back during that period adds the configurable timeout.
I am unable to reproduce that, neither on HD-FOX nor HDR-FOX.
I have my HD-FOX set to the 5s default, and the channel change banner does indeed come up for 5s – although it took me a while to realise it is as long as that, because it precedes the new channel appearing and even the old channel disappearing! I would not describe it as "cumulative", it simply restarts if you change channel again within the timeout (cumulative would be if it adds another n seconds on top of the current countdown).
Equally the i button timeout is (I agree) 30s, that timer restarting at each command input (i for more info, or cursor for info on subsequent programmes or adjacent channels).
The OK button produces a channel list, also with a 30s restarting timeout.
The Menu button has a 3 minute timeout (actually a couple of seconds less than 3m), ditto Media and Guide. It's all rather a mess of arbitrary choices made by committee without providing customisation options, although one can see the rationale for Menu, Media, Guide – further user input is expected once presented information has been digested.
I wondered what else might respect the user setting. V-Format and Wide produce 3s pop-ups... so it seems nothing else does.
Curiously, the menu options for "Screen Display" are from "OFF" to 20s in 1s increments. I can't imagine anyone would be that bothered: "14s is just right, but 13s is too short"!
In the manual, it's clear what the scope of this user-configurable timeout is:
You can set the duration the information box is displayed every time the channel is switched.
...so "there's nothing to see here" (except perhaps lack of clarity in the settings menu wording).