People, people.... (shaking head)........
The filter pad is a major home for beneficial bacteria. You don't need to change the filter pad until it's just about falling apart for that reason. It serves as biological and mechanical filtration, the carbon has nothing to do with that! You remove the carbon after a couple of weeks by making a hole in the filter pad and shaking it out. You don't need to run carbon. The op is correct in his belief that changing out the filter pad was a bad move.
Username, you musta stirred up some kind of decayed crap the other day to get such high nitrates. You've been on the right track with how you care for the filter, but there is a much better way to maintain your tank. It also occurs to me that with the topping off and the infrequent and large water changes over time, you may be susceptible to old tank syndrome. Your pH looks okay right now, though. Just something to think about.
Better maintenance can help avoid problems in the future, but it doesn't answer exactly what has happened this time. However, you'll have a healthier, more stable tank over a longer period of time if you vacuum your gravel with every water change, and do 20-25% water changes every week to two weeks, depending on your nitrate readings. Keep them below 20. Continue with your filter pad maintenance by not replacing it until it's worn out, simply rinsing it in a bucket of tank water as you have been doing. Never, ever, ever change your filter pad the same time you clean the walls of the tank, the ornaments, and the gravel -- you could indeed wipe out all the bacteria, as you are aware! (just some FYI's for less experienced fishkeepers) Instead, maybe clean an ornament or two at a time, vacuum the gravel weekly, scrub the sides before water change one week, do only one of these things at a time, and never when you have to change the filter pad. I've seen so many people kill their fish by doing a gigantic cleaning job on their tanks.
I wish I could offer more specific help on the current situation. Jo3 is quite knowledgeable and experienced, and you can see we have lots of members willing to help. Hopefully some of our more experienced members will add their two cents soon.