meaning - Some questions about って

Here is a sentence from Dragon Ball :

一気にこれ以上修業したって意味はないって。限界までやったんだ。

悟空 says this to his son who's worried because they just chill out before a battle instead of training until the last minute.

As far as I know, the second って means と言っている and is used to insist on what precedes it, like : "And I'm telling you that..." in english. Am I right here?

As for the first って, I don't know if it means という, or even というのは :

I'm telling you that it wouldn't have made sense to train more than that without pausing.

Or if, as I think, it's part of たって meaning ても :

I'm telling you that even if we trained more than that without pausing, it wouldn't make sense.

Is there a way to tell one from the other when a word like 意味 comes after?

Answer

「[一気]{いっき}にこれ[以上修業]{いじょうしゅぎょう}したって[意味]{いみ}はないって。[限界]{げんかい}までやったんだ。」

"As far as I know, the second って means と言っている and is used to insist on what precedes it, like : "And I'm telling you that..." in english. Am I right here?"

Right. The second って is quotative, implying "Here is what I want to say and I know what I'm talking about.".

"As for the first って, I don't know if it means という, or even というのは"

"Or if, as I think, it's part of たって meaning ても "

It is part of たって, which is the informal way of saying ても or たとしても. These express a non-resultative hypothetical condition, which is why your TL:

"I'm telling you that even if we trained more than that without pausing, it wouldn't make sense."

could not be any better.

"Is there a way to tell one from the other when a word like 意味 comes after?"

You would need to look at the whole phrase, not just the single word, following the って -- in this case, 「意味はない」. If the phrase after the って seems contradictory to the phrase before, you have what I called the "non-resultative hypothetical condition" above. In the sentence in question, the two phrases are "to train hard" and "it is nonsense".

I could, however, easily form a sentence containing a 「って意味」 in which って actually can be replaced by という rather than by ても or たとしても.

「その[単語]{たんご}に『[食]{た}べる』って意味はないよ。」= The word does not have the meaning of "to eat".

So, you would need to pay attention to the whole context as usual.