The Seecamp 32 LWS is designed to accept cartridges no longer than 0.91", and Larry Seecamp has put a spacer in the magazines to ensure this length works well. He has a complicated explanation on his web site which doesn't explain much, but basically the length and spacer are there to prevent the semi-rimmed cartridge rims from overlapping each other and hanging up. The 32 ACP can come in many lengths, so knowing which is which is important.
Mine has worked well for 24 years with no malfunctions using his recommended loads. Check his web site for recommended cartridges. Those are simple explanations and worth reviewing.
You own the current box - try them and see if they work. If they do, then they're fine - they're within the length tolerance. If they don't, no harm done pressure-wise, they just might not function in the LWS.
Last edited by Jaywalker; 04/05/13.