Sorry, that's too easy to misunderstand.

Let me be more precise:

$b = $a with = overloaded to ->clone will not do an immediate $b =  $a->clone °

It's rather a kind of copy-on-write.

After the assignment the refs will still be identical : $b == $a

The ->clone ("copy" in COW) will only happen delayed just prior to changing $b or $a ("write" in COW)

see https://perldoc.perl.org/overload#Copy-Constructor

$a = $b;
# ... (other code which does not modify $a or $b) ...
++$b;
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would be executed in a manner equivalent to

$a = $b;
# ...
$b = $b->clone(undef, "");
$b->incr(undef, "");
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But the wording is fuzzy and needs to be tested.

Anyway this could indeed fix the problem of the OP in an efficient way.

°) In Math::BigInt the cloning is done with the method ->copy