equivalent regular expressions (e.g. /.../ and /.{3}/ should end up the same

Evidently, you did not try this out yourself before posting. It took me 10 seconds to see that

% perl -Mre=debug -e '/.../'
Freeing REx: `","'
Compiling REx `...'
size 4 Got 36 bytes for offset annotations.
first at 1
   1: REG_ANY(2)
   2: REG_ANY(3)
   3: REG_ANY(4)
   4: END(0)
minlen 3
Offsets: [4]
        1[1] 2[1] 3[1] 4[0]
Freeing REx: `"..."'
[download]

and

% perl -Mre=debug -e '/.{3}/'
Freeing REx: `","'
Compiling REx `.{3}'
size 4 Got 36 bytes for offset annotations.
first at 3
   1: CURLY {3,3}(4)
   3:   REG_ANY(0)
   4: END(0)
minlen 3
Offsets: [4]
        2[3] 0[0] 1[1] 5[0]
Freeing REx: `".{3}"'
[download]

are quite different beasts. So that's not going to fly. Unfortunately, I don't have any better ideas myself. The only thing I can think of would be to take a look at japhy's Regexp::Parser, which will ease the pain of picking a pattern apart, but to put them back together again with an eye to checking for equivalence will be non-trivial.