I decided on the Logitech G600 Gaming Mouse (~$80 USD) as the replacement. This mouse supports Logitech's Gaming Software. I plugged it into my computer and it recognized the mouse without having to install any drivers, and I still had all my profiles from my old mouse.
The mouse can have 5 DPI settings per mode and there are 3 modes per profile. The DPI range is 200-8200.
This mouse has 20 buttons with 18 of them being customizable (you can change all 20, but you have to have a button for left click and another for right click). There is also a function called "G-Shift", which is like a second page of macros for the profile. This means that you can have 34 macros on this mouse per mode (you must have buttons dedicated for left and right click, plus one button has to have the G-Shift function assigned to it).