Never practice something doing it with mistakes.
In this respect, "bump up the metronome past your limit" might be misleading. If this causes you to repreat a phrase wrongly, it is not the way to go.
I think the intent of that advice is to rather to try to find a smaller part of the phrase that you can do past your current limit for the whole thing.
Take the classic "1234" finger/alternate picking exercise.
I can go
-----------
-----------
-----------
-----------
------5678
-5678------5678
much faster than I can go
--------------------------5678
---------------------5678
----------------5678
-----------5678
------5678
-5678------
It is useful to both
1) Work on the second thing bumping up the metronome till you make a mistake then back off. This is like your method 1. This makes sure that your skills are consolidating
2) Find smaller things like my first example that you can do much faster, and push the envelope. Expand them gradually (like in this case adding a string).
This makes sure you are actually pushing the envelope and getting better. "reaching for higher speeds" as you said.
IMHO. YMMV. HTH.
GaJ