That perforated back would turn on a red light for me concerning the speaker components inside - I would interpret that 15 watt rating as meaning not very good. Could be wrong, but those two factors in my mind point to a lowish end speaker enclosure and therefore makes me imagine the cabinet material is utility grade particle board or MDF and on the thin side. If so, beefing it up internally with another layer on all sides would make them less resonant for use with a better woofer. Plus a new, non-perforated cabinet back. From what you've just written, it sounds like they were tables first and speakers second.
Is there any sound absorbing material at all inside them as they are?
If this were my project, I would calculate internal cabinet volume and use that number to explore new woofer possibilities. And to narrow down the field and make things easier, I would probably plan on sealed air suspension boxes instead of ported bass reflex. Comparing internal cabinet volume with that required by potential woofers would show if there are many or few candidates.
You may get away with using the existing front baffle board. Those cabinets might not lend themselves easily to removing the grill covering, exposing the drivers so you may be restricted to original woofer diameter and mounting hole pattern. There are ways to overcome the latter, just need to be creative.