The alternation between Angle and English is regular, umlaut of the e by the following i, as in Frank ~ French, or (much earlier) man ~ men.

The change from Eng- to Ing- must have been early, possibly before o-umlaut changed to e in Old English, because strength and length didn't change (both from -o- of course). There are no other normal words in English containing -eng-. There's an obsolete word 'meng' (= mix, mingle) but this has the alternative 'ming'. Modern words like 'penguin' and 'Dencorub' show it's perfectly pronounceable, but it must not have been a thousand years ago or whenever.