You can draw the cards in a random order by using the output of an accumulator fed to a block cipher as an index. The fixed output size of a block cipher does entail extra work in filtering numbers outside the range you'd like, just as you would with an LFSR. (as a direct power of 2, you could directly use an LFSR or some ECB-mode block ciphers as if it were format-preserving, but that is "coincidence").

You can produce an exact random permutation with a Feistel network for any number, in this case selecting every number between 0 and 2^64 exactly once, with no appreciable space requirements.

   procedure feistel(input) {
      result = input;
      h = 2<<32;
      for (let i = 0; i < 8; i++) {
          l = (input / h)|0;
          r = input % h;
          temp = r;
          fn = (r + i) % h;
          r = (l + fn) % h;
          l = temp;
          result = h * l + r;
      }
  
      return result;
  }