I note this is mathematically incorrect.
[...]
Not casting 30 votes is actually harmful by increasing the relative power of other voters over yourself.

It's not harming anyone except you assume an attack to be going on. It's not necessary to exert the maximum influence, you do not lose anything as there's nothing to be gained from voting witnesses. Or do you see the amount of vests you contribute to the total voting as some form of currency or badge?
From another reply:

So what is the effect of switching a vote exactly?
Removing a vote from a top witness: doesn't influence anything at all, as long as it doesn't make it drop out and someone else get in
Adding a vote to a top witness: doesn't change anything except making it harder for backups to replace them
Removing a vote from a backup witness: lowers the rewards for that one, raises the rewards for all other backups
Adding a vote to a backup witness: raises the rewards for that one, lowers the rewards for all other backups

It's definitely possible to find 30 underrated witnesses, but it takes time. It's better to avoid voting when not informed, and add votes one by one.

Does voting on an HPS proposal directly also withdraw proxy?

I would expect that.