All native English speakers will think "the more early" and "the earlier" are very weird.
There are two basic ways that you can use a comparative form in English. For example. "friendly" is an adjective. And in English I can say "more friendly" or "friendlier". But there are some adjectives where I must say "more [adjective]" and some adjectives where I must say "[adjectiv]-ier" and I think these can only be learned from memorization.
In your case, "early" wants to use the comparative form "earlier" though "more early" does work.
So I would say "Last night, I went to bed earlier than my friend did" but if I said "Last night I went to bed more early than my friend did", it would be completely understandable.
You cannot add the "the" to those words, though, because it is very unnatural there. I know that it is very tricky, but you may consider to limit the use of "the" when you are talking very specifically about a specific subject of a sentence or a specific object of a sentence. There are exceptions!