The other parsers deal with ambiguity by throwing it away. So, no, they would not have a problem with excessive ambiguity. :-)
An interesting question is if the only parse not thrown away is actually the one you want. If I read the code correctly, you're not actually evaluating the expressions. I think it would be important to do so, and to see if they all produce the same answer.
Also, I note that all test examples are of the form "1+1+1+ [...]". As
the blog post Ruslan mentioned details, Marpa::R2 has a higher constant than regular expressions, but is linear for more grammars than any other parser out there. So the pattern is that regexes are a huge win on the simple ones, and a huge loss once regexes start going linear.