You are very correct in your thinking about how guitar and piano practice produce simialr results. If you practice long enough, you will succeed.

As to why arpeggios are easier for you I would speculate it is that you have to grab the entire chord all at once. Not one string at a time. This involves training your Muscle Memory to do the heavy lifting. Like piano, that takes time and persistant practice.

I learned how to do this by memorizing the patterns of the chord I wanted to work with. Getting those patterns into my head was the first step. Then I started practicing grabbing the pattern on my fretboard. No strumming yet.... In off hours (like watching tv) I would simply jump around to those chord patterns, without strumming them. Get those patterns drilled into you Muscle Memory, until you can easily and accurately change between them. I used to practice grabbing patterns in slack time by grabbing fingerings using my right forearm as a practice neck and grabing those chord fingering on the forearm with my left hand. I kept changing them until it was drilled into my fingers. Only then did I get serious about taking this skill to apply to real songs. Go slow at first. Gradually increase your speed until you have mastered the song.

As to how long it will take you, you are better at simply accepting that you will get it as soon as your body is able to do so...no sooner. I repeat... NO SOONER. To further complicate thak kind of thinking... everybody learns at their own pace. So it is completly impractical to attempt to project how long it is going to take. The sooner you give that question up... the sooner you will develop skills.