I agree on the two-step approach (at least for now ¹), but I'd reverse the specificity of the regexes: I'd first do the validation using a specific regex and in a second phase split out the data you want from the capture in the first, which might be using a simpler regex because you validated the data already:

while (<DATA>) {
    my ($params) = /^foo ((?:m \d+ *)*) bar$/;
    my @nums = $params=~ /\d+/g;
    print "$params -> (@nums)\n";
}
__DATA__
foo m 1 m 2 m 3 m 4 bar
foo m 2 m 4 m 7 bar
foo m 1 bar
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¹ Looking at demerphq's slides on his work on extended regexes in Perl 5.10, it might become possible to have a simpler, single step solution in the near future. See %-.

But maybe I'm just dreaming.