(S)he is indeed claiming that "友だち would be more 仲良し than 恋人".
Here's my attempt at translation:
なんかさ… 別れてから 友だちに戻って 実はちょっと 嬉しいとき あったんだ
How would I put it... After we broke up and went back to just friends...
I Actually was a little happy.
…なんか そーゆーの 友だちとか 恋人より もっとずっと 仲良しって 感じしない?
Like, you know... being friends... has this feeling of being much more close than lovers, you see?
Unfortunately 仲良し does not have an exact equivalent in English and may be somewhat difficult to distinguish from 友だち/friendship.
The root of it is 仲{なか} (relation; [close] relationship) which is also used in the following words among many others:
- 仲間{なかま} - friend/partner/colleague/comrade
- 仲{なか}直{なお}り - reconciliation; making up (e.g. after a fight/break up)
- 仲間{なかま}入{い}り - getting accepted into/joining a group (e.g. of friends)
- 仲人{なこうど} - matchmaker
- 仲間{なかま}はずれ - being left out; being ostracized
As another example, 仲{なか}がいい is also used when describing siblings or cousins who help and respect each other, don't fight etc.
EDIT
By popular demand, let me try to clarify the terms a little more.
While 仲良し can be used as a type of relationship on its own (probably somewhat analogous to "best buddies"), in this case it's used as a qualifier on the closeness/intimacy of the relationship and is not a stage by itself.
Both 友だち (friends) and 恋人 (lovers) can be 仲がいい (on good terms) or 仲が悪い (bad terms/falling out/cats and dogs). E.g. in the latter case the friends may have had a quarrel over something or "lovers" could be in an abusive relationship and only stay together due to some external factor.
Now, assuming you were on good terms (仲がいい/仲良し) in both cases, how would being friends be a closer relationship (もっとずっと仲良し) than lovers?
This is a little difficult to answer without reading the work, but going by the common tropes I've seen in manga, during the 恋人 stage there could be a more heightened awareness of the other party or the opinion of the people around (緊張 - tension/nervousness), or the implied pressure of having to be considerate (気遣い), while 友だち is usually a more relaxed environment where each can be closer to their true self and more open, which could make it feel more close or intimate.