I've attached a patch for adding the -scope option to info variable.
The code ist copied from Itcl_ScopeCmd() and slightly modified
to work in the info environment. As written before, it's not perfect
and should only demonstrate a path to fix this ticket.
With this patch it isn't possible to get the scope of
single array variables, only the name of the whole array works.
Also I've done very few tests. If this is the way to go,
I'm willing to put more work in this solution.

I attach a little test script infoVariableScopeUsage.tcl which
demonstrates the usage of -scope option.

The output of my patched version of Itcl4.1.1:

Itcl=4.1.1
_baseV1    scope = ::itcl::internal::variables::oo::Obj15::Base::_baseV1
_baseArray scope = ::itcl::internal::variables::oo::Obj15::Base::_baseArray
_baseArray get   = two 2 one 1