Since I can’t rely upon “that version of Perl,” my present train(-wreck) of thought is to either bring in a separate random-number object for this purpose, or to do the “re-seed with a random number picked just before re-seeding” strategy described earlier.   (It is good to know that Perl is getting this “return the previous seed value” capability, as many other languages do have it, but it’s too late for this (cr)app.)

Thanks for your inputs, one and all.   Now, back to the coal-mines.

It sounds like you're getting wrapped up in a few problems:

1. You've got code that depends on a stable list of pseudo-random numbers.
2. The pseudo-random numbers aren't random enough and the results are skewed.
3. There are calls to srand($n) throughout the program.
4. You want to capture the "state" of the RNG at various points.

So tackle these problems separately. As a kludge, you should be able to make the program run as-is, but with better results.

1. Follow JavaFan's (and others') suggestion and pre-generate a list of better random numbers. There are more elegant ways to do this, but for the sake of the concept, store a list of a million pre-generated random numbers in the __DATA__ section of the code, pull them up from <DATA> and put them in a global array @RAND, accessed with a global $COUNTER. External sources might complicate matters at this stage, which is why I suggest throwing it in the code.
2. Then borrow Tye's suggestion to override srand and rand for your purposes:

   BEGIN { 
     our @RAND = ();
     our $COUNTER = 0;
   
     for (<DATA>) {
       $_ += 0;
       push @RAND, $_;
     }
   
     *CORE::GLOBAL::srand = sub(;$){ $COUNTER = 0 }; 
     *CORE::GLOBAL::rand  = sub(){ return $RAND[$COUNTER++] };
   }
   [download]

3. Now srand($n) will ignore $n, but will reset $COUNTER so the sequence can start again. And rand will act as expected, but will return the number from @RAND rather than generate it on the fly. From the perspective of the rest of the code, this should be transparent, obviating the need for global changes (as in search/replace) to the code.
4. To capture the state of the "RNG" (now a list), simply capture $COUNTER to pick up where you left off later.

--marmot