I had a pair of Large Advents of the same vintage and the woofers required repair about 20 years ago.. I'm surprised your woofers lasted this long.
Send both woofers in for repair and you will be fine. If you want to keep them until you die the Simply Speakers replacement woofers are the best fix. The cost is reasonable. Even if you decide to upgrade your speakers, those Advents are collectable and people will pay a surprising amount of money for them if the cabinets are in good shape. I sold mine with repaired woofers for $300 but the cabinets and grills were in perfect condition. I see them selling on eBay for as much as $450 a pair. If the cabinets are trashed it's a matter of how much emotional attachment you have to those speakers. There are hundreds (thousands?) of used speakers available for under a thousand dollars a pair that will sound quite a bit better than your Advents.