I also want to distinguish between GMP objects and simple integers

Yes - inside my own gmp-based modules I often want to know about such things.
I normally use XS or Inline::C subroutines for this.

In pure perl code, as you may already be well aware, the ref() function will go a long way to providing useful information about references and module objects.

use warnings;
use Math::BigInt;
use Math::GMP;

my $v = 9;
my %h = (foo => $v);

for (\%h, [$v], \$v, Math::GMP->new($v), Math::BigInt->new($v), $v) {
  ref($_) ? print ref($_), "\n"
          : print "Not a reference\n";
}

__END__

Outputs:

HASH
ARRAY
SCALAR
Math::GMP
Math::BigInt
not a reference
[download]

You can also use the B module instead of XS/Inline::C to determine whether a scalar is an IV or an NV or a PV or a combination thereof.

If you want more info on any of these aspects, just ask.
(I don't want to annoy you by banging on with stuff that you already know (or stuff that you're not particularly interested in).

Cheers,
Rob