There is a fairly simple fix for this objection, and it doesn't require many different types of ordnance. Each weapon component should have its own ordnance storage capacity and not 'share' with any others. Basically, this turns ordnance in a 'number of shots' counter for each weapon that uses ordnance. That means each weapon would represent both the actual firing device and the ammunition storage capacity, which is how seekers currently work in SE IV anyway.
I happen to like the idea of needing some 'generic' cargo space for ammunition in a warship but it's not essential to the concept of ordnance.