The strut mounts are defective from the beginning. By now you should also change out the struts along with the mounts. Avalon back then was just a bloated Camry, so you have the same problem.
Some in the newsgroups are happy with the Monroe SensaTrac. If you do too then you can buy their "Quick Struts" complete with SensaTrac struts, springs, mounts, boots, etc. Just swap them out -- quickly -- and then get an alignment. I think these Quick Struts are guaranteed lifetime? Check
formatting link
and
formatting link
I personally don't care for the el cheapo KYB (Keep Your Bilsteins) that are often used as stock struts. It's plain without any decent valving. But if you want a cheap strut it's also got lifetime guarantee (like pretty much all the other name brand struts).