oo-ee change for plurals

Question

The plural of tooth is teeth but the plural of booth is booths.
The plural of goose is geese but the plural of moose is moose.
The plural of foot is feet but the plurals of root, boot, and toot are roots, boots, and toots.

I have ascertained from my research that whenever an oo word changes its plural form to ee, that word traces to West Germanic. The counterexamples come from different languages.

Questions

How did these irregular nouns come to be?
When was an oo to ee change first attested, and why didn't the West Germanic speakers simply add an s?
Is there any significant linguistic research on this topic?

Some places I researched:

Oxford Dictionaries: Why is the plural of ‘moose’ not ‘meese’?
EL&U: "Goose"–"geese" vs. "moose"–"moose"
SpanishDict: Why moose in plural is moose, and goose in plural is geese?
Quora: If the plural for goose is geese, then why isn't the plural for moose "meese"?
Why is it feet and not foots?
Yahoo! Answers: Why isn't the plural form of "foot" simply "foots"; just like everything else on our body? (i.e. Hand/hands)
Wikipedia: West Germanic languages
Encyclopædia Britannica: West Germanic languages

This is not a duplicate because the post in question, Why is the plural form of Moose not Meese?, doesn't answer my question: I want to know how the oo-ee change occurred in West Germanic, and the answer on that only briefly touched on this topic.

Since you ask, here's the answer. This only happened to a few words; it was a long process that took centuries if not millennia. — John Lawler, Mar 15 '17 at 15:05
You may also be interested in the other posts with the tag i-mutation — herisson, Mar 15 '17 at 15:15
German is as close to West Germanic as English is, and these are English grammar rules I'm questioning — etymologynerd.com, Mar 15 '17 at 15:24
You may ask the linguistic site. http://linguistics.stackexchange.com/ — , Mar 15 '17 at 15:30
@etymologynerd.com: have you seen the Wikipedia article on Germanic umlaut? I think it could be helpful. — herisson, Mar 15 '17 at 15:31
@Josh, neither of those other questions go nearly as in-depth as my question necessitates.; I really don't think it should be marked duplicate. Though moving it to the linguistics site doesn't seem too bad of an idea; how do I do that? — etymologynerd.com, Mar 15 '17 at 16:18
I agree, but, most of all we have a Linguistic site for questions on like this one. — , Mar 15 '17 at 17:41
@etymologynerd.com John Lawler’s answer to the question this is currently marked as a duplicate of details the individual steps in the development of i-umlaut quite specifically. My own comments to his answer also help in answering your questions. Is there anything specific that you feel is not answered by that, except perhaps the bit about research on (West) Germanic i-umlaut (of which there is a lot)? — Janus Bahs Jacquet, Mar 15 '17 at 19:16
A good place to start (though it deals with Proto-Germanic rather than West Germanic) is section 3.2.5 in Donald Ringe’s From Proto-Indo-European to Proto-Germanic. — Janus Bahs Jacquet, Mar 15 '17 at 19:22

oo-ee change for plurals

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