My feeling as a native speaker is that for your second interpretation
"You may perhaps do it better by yourself." = "do a better job of it"
you would, in good everyday German, rather use
Vielleicht machst du das alleine besser.
Like in English, the position of the word at the end adds emphasis to it. In spoken language there would be also strong emphasis on "besser" by intonation.
I would not fully exclude that for your
Vielleicht machst du das besser allein.
in the above sense you may find a concrete situation in life where this could be used. But, then, when I try to come up with such a situation I find it extremely difficult.
Perhaps it could appear in some dialogue where the topic of "should I do this together with others, or should I better do it by myself?" has already been discussed in detail so that it is utterly clear to everybody that this is the topic.
Let's try and build such a dialogue:
A: Den Bericht zu schreiben zusammen mit drei Kollegen, das ist wirklich mühsam.
B: Ja. Berichte im Team zu schreiben ist wahnsinnig zeitaufwendig. Die ganzen Diskussionen immer. An jedem Satz diskutiert man da rum.
A: Ich glaube, wenn ich ihn alleine schreibe, wird er besser.
B: Ja, du machst es besser allein.
Uh... and still, in order to tranfer the meaning "By myself I will do it better", this needs special emphasis by intonation on "besser". Otherwise even in this dialogue the immidiate understanding would be "Perhaps I'd better do it alone".
Well. I am disappointed now. I feel that my attempt to find a situation where the meaning "By myself I will do it better" would be expressed like this has failed...