in-, en-, im-, em-, il-, and ir-: almost morphological nuts

Uncontent with my venture into the nuts of negative prefixes, I awoke this morning thinking about assimilation.

It struck me that in- changes by assimilation in some circumstances. In my half-awake state I ran through the obvious ones
irrespective
improper
immature
imbalance
illegal

which was uncontroversial until I (incorrectly of course) thought of input.

The in- in input is of course a locative prefix, not a negative. Undoubtedly it follows dissimilar rules, so I then tried to envisage some locative in- words to explore those, like
irradiate but inroad and inrush
impact but input and inpour
immerse but inmate
imbue but inborn
illuminate but inlay, inlet and inland
which imply that in some instances, locative in- assimilates identically to negative in-. Except when it doesn’t.

Bauer, Lieber and Plag (2013) in their Oxford Reference Guide to English Morphology has a short incursion into prefix allomorphy in pages 179 and 180, in which they explain that with the negative in- such assimilation is ‘obligatory’, so
in- + labial consonant (b, m, p) = im-
in- + r = irr-
in- + l = ill-.

However they also survey usage in a large corpus (COCA), where they find the word inbelief, rather than imbelief, and the OED has ample historical uses of negated words starting with inm- and other breaches of the obligation. They seem to avoid the more complex issue inherent in the locative in-, though.

One common factor among those locative in- prefixes is that those which assimilate did so before reaching the English language, inborn in Latin origins, whereas those which have not assimilated – perhaps dissimilated? – seem to have been formed initially in English, with stems from Old English.

A further twist is that the Greek locative prefix was not in- but en-. So does that follow the same rule as Latin locative in-?

Emphatically yes:
ellipsis
empyrean
emblem
embolism.

So here is my working rule for the in- (and en-) prefix in English:

  1. Is the in- a negative? If so, assimilate with leading b, m, p to become im-, with leading r to irr-, or with leading l to ill-
  2. If not, and it is a locative, is the word derived from a Latin or Greek word which comes with the prefix already attached? If so, follow the assimilation of its origin (which will be the same as in 1)
  3. If a locative and it is a newly formed compound in English, then do not assimilate.

If you can think of an exception or inception, please let me know immediately.