The capitalized Old Japanese (上代日本語) certainly has two vowel-stem types of verbs that yield today's -eru/-iru verbs respectively. However, it's not accurate to say they end in -e/-i because the language in the Old Japanese stage had 8 distinct "vowels", or to recent understanding, more like "rhymes":
a, i1, i2, u, e1, e2, o1, o2
which merged into the current 5-vowel system by the 9th century (then it becomes called Early Middle Japanese).
The two stem-final vowels you mentioned are actually -e2 and -i2, both of which were formed by contraction of adjacent vowels which are thought to have existed in earlier, pre-document ages. Since I don't have access to books such as Frellesvig (2010) now, just let me quote Wikipedia for an overview:
- i2 < *ui: kami2/kamu- 'god, spirit', mi2/mu- 'eye', nagi2/nagu- 'a calm'.
- i2 < *əi: ki2/ko2- 'tree', yomi2/yomo2- 'Hades'.
- e2 < *ai: me2/ma- 'eye', ame2/ama- 'heaven', ame2/ama- 'rain', kage2/kaga- 'shade'.
Thus you can presume that some vowel-stem verbs were actually composed by underlying bases that end in other vowels, and suffixing *i.
aka "red, bright" / ake2- "brighten"
oko2-s- "raise up" / oki2- "arise"