I don't have a LiLi but I do have a fair bit of anti-vibe experience. For the best chance at reducing the vibes, you need to put grommets in the holes you drilled. Actual A-V grommets are best but regular wire grommets should help. Go to Mcmaster for the A-V grommets, the size highlighted should cover most applications. It's the grommet on the right in the pic below.

Lets use your pump mount for an example, the screw head touches the hard plastic and the nut touches the mount, your gonna have a rattle...if the ends of those screw touch that divider, your gonna have another rattle. You'll likely have them even if they don't touch due to the way the mount appears to be attached. The grommets work by isolating any metal to metal/ metal to plastic contact and is why they need to be in the holes. Another way to kill rattles is to use that thin sound absorption material almost every store sells, it's not really as useful for actual "sound absorption" as much as it is for "rattle prevention". Fill the case with it and every little annoying rattle pretty much disappears.