org-mode agenda view with late recurring tasks at top - emacs

Question

I have some TODO's in my recur.org file which look like this:
** TODO Do this thing every day.
SCHEDULED: <2016-09-19 Mon .+1d>
For me, that . before the +1d means "if you happen to do this job late, then when you mark it as done it will re-schedule itself to the day after when it was marked as done." This is correct, because this job does have the property that if I don't do it for 4 days, then I don't need to do it 4 times to catch up, I just need to do it once. On the other hand, if I don't do it for 4 days then I really need to get this job done and I would hope that it gets flagged up in red when I look at my weekly agenda view with C-c a a in emacs org-mode.
Unfortunately, this does not happen. The standard agenda view lists this task as
[stuff in red here with Sched. 4x etc etc]
recur: Scheduled: TODO [#A] Do this thing every day
and the entry is in green with no indication that I'm late. This is presumably because the fact that it is scheduled every day means in particular that it is scheduled today, and so hang the fact that it's still also scheduled 4 days ago.
This is not the behaviour I want. I would like to be able to make a repeated TODO which, when done, resets the scheduled time to today+[interval], and yet I am still warned if I fail to do the task for a time period which exceeds the interval.
Experiments indicate that jobs with things like .+1w behave the same way -- they're 6 days overdue and then all of a sudden they're not overdue any more.
Could I write a custom agenda command somehow, to ensure these jobs are flagged when they are late?
Added 3rd Oct: Some further experimentation has revealed that the dot isn't the problem -- this is also the default behaviour with recurring TODOs that just are due to be rescheduled after a time delay shorter than the time it's taken me to fail to do them.
However I am now slightly more optimistic that this can somehow be solved with a custom agenda view. For C-c a L gives me a view where the recurring task shows up on the first day it's scheduled and not done, rather than the most recent day it's scheduled and not done. However C-c a L is no good for three reasons: (1) it shows tasks which are DONE (2) it shows priority C tasks which are late (and I am much less interested in these) and (3) it only acts on the current buffer. So if I learn enough about agenda views I feel like I might be able to answer my own question.
Added 9th Oct: Having now read the relevant pages of the org manual I realise that I still do not know how to do this. I am surprised. What I am asking for is an agenda view which encompasses all my org files, gives me a weekly agenda like C-c a a, and which flags the first not-yet-done occurrence of each repeating TODO task which has priority A. From a purely logic/programming point of view I don't see any obstruction to this, and I would be quite surprised if there were no way to do this in org-mode, but I certainly can't find it. Help!