I'm running official JB rom (rooted) and after a bit of tweeking it is running fine, with minimal lag. My memory usage is the same as yours, so I don't think that is your primary issue.
I suggest you do the following (as I did) :
. Backup all your apps and data using Titanium
. Factory reset
. Use the phone for a while without restoring to ensure there are no hardware problems. Performance should be good.
. Restore the essential apps you use. Again, use the phone for a while to ensure it runs without lagging.
. Restore the rest of the apps one by one.
In my experience the primary reason for the phone lagging is too many badly behaved apps that either use too much memory or hog processor time via wakelocks, etc.
Badly behaved apps unfortunately include some bloat that Samsung put on your phone by default. I had to disable (freeze via titanium) some samsung apps, such as Vlingo before my JB worked well. Use wakelock detector and cpu stats to determine which apps are misbehaving. If you just leave your phone alone most of the day you should be seeing around 70% deep sleep.
Good luck. Hope you get it sorted. I was about to trade up my note for a note 3 but after the optimisation I don't think I'll bother for a while because now my phone runs very well and make no mistakes, I am a heavy user.