this is actually explained by something called the Indo-European ablaut, or as the Indians who original came up with this call it, Guna and Vrddhi. Basically, there is a set of vowel grades in the IE languages: a -> (long) a -> (long) a; i -> e -> ai; u -> o -> au; (vowel) r -> ar -> (long) ar. The reason for the ablaut changes are fairly complex, but notice how in your example reign has the "e" as in pain, whereas "sovreign" has the "i" as in "bit", reign is actually the "guna" or first grade of the ablaut. English spelling doesn't generally represent these changes, nor does it have to, because people are aware of the sequence without knowing it, and those sound changes do not sound strange or out of place for them.

>scholars presuming the etymologies are linked and adjusting their spelling to reflect that

English actually has no official spelling for any words, its just that the King James bible was the first widely distributed printed book that people were able to read in the English speaking world, so people adopted the spellings for words in that book. Its quite arbitrary, which makes the elegance of the spelling system even better--the fact that no one got involved meant that we were able to create this beautifully complex system that could represent nearly an infinite number of sounds, because nobody tried to "standardize" and phoneticize English spelling.