| It's a pity it's not possible to force MEME to find 100% conserved positions, but this still gives me something very close to what I want.
Finding exact matches to a given regular expression is pretty simple in any of the popular scripting languages. In the MEME Suite command line tools we include
fasta-grep for this.
| Also, is there now any way to find a motif that is present "two or more times" (or ideally "n or more times") per sequence, rather than OOPS?
MEME has three models for the number of motif occurrences in a sequence database: OOPS (only once per sequence), ZOOPS (zero or once per sequence), and ANR (any number of repetitions per sequence).
However, that doesn't seem to fit what you are asking for. If you are limiting yourself to exact matches of a regular expression it would be pretty easy to implement in a script.