Place text next to rehearsal mark, or with left edge over barline if there is none

[caagr98]

As you can see on the screenshot, both texts are misaligned. The first 
one, a \tempo, is placed *under* the rehearsal mark instead of next to 
it. The second one, the name of a song, is too far too the right, since 
it's attached to the note instead of the barline (it's a <>^"").

How can I move the texts to be next to the rehearsal mark (without 
manual adjustments)?

And is there a version of <>^"" that is attached to a moment instead of 
a note, to be more semantically correct? I think \mark is supposed to do 
that, but it only supports one mark at a time.

2017-07-09_18-13-35.png
Description: PNG image