I think you can think of 的, 得, 地 as suffixes that indicate parts of speech. Basically, 的 is used after a noun or an adjective, 得 after a verb, and 地 after an adverb. Unlike 的 and 得, which have their root in Chinese history, the idea of 地 used as an adverb indicator is relatively new; it was borrowed from western languages. It's probably intended to imitate the -ly ending in English.

When you use the “adv 地 V” structure, it describes one single action and that's it, and the verb is normally followed by a particle or/and an adverb when the verb has only one character. Take for example the first sentence in your question, an particle of 著 or an adverb of 開 or 掉 should be added to the verb 走 so that the sentence would sound natural and complete.

When you use the “V 得 adv” structure, you are making a conclusion or stating how you feel about the action described. I don't know if a little literal translation will help better, but I'll try anyway. The original meaning of 得 is “to get”. Therefore, a word-for-word translation of 他走得很慢 is “He:他 walk:走 (and) get:得 (a result of being) very slow:很慢”. The result or conclusion of him being very slow is quite subjective.

Therefore, the “adv 地 V” structure is a “cold” statement, like it's made by a biologist observing an animal. While the “V 得 adv” structure is a “warm” statement, it shows how the speaker subjectively feels.

Here are other examples: (雨: rain; 很猛: fiercely; 落: fall; 下: down)

雨很猛地落下。
→ The speaker is making an objective observation of how the rain falls/fell. And the verb 落 is followed by an adverb, which is 下 in this case, to make the sentence sound more natural and more complete. It's a “cold” sentence.

雨落得很猛。
→ The speaker is describing how he personally feels/felt about the way the rain falls/fell. The rain makes/made him think so. It's a “warm” sentence.

PS There's an official plan to integrate 的, 得, 地 into one, which is 的, but I don't think it's settled already.