It seems possible, although challenging; I'm curious for your take on this:

0. You run a large network with substantial hash power.

1. You submit a transaction that is broadcast only to your own mempool and don't relay it outside of your network.

2. You attempt to include this output in some/most/all attempts.

3. You finally solve a block with this transaction and distribute it to the rest of the network.

If this were happening, one way to surveil for it would be to keep track of every submitted transaction that a few nodes ever see. Is there a mining pool that is consistently mining huge fee transactions that were never present in your mempool?

If you've already mined the next block, then you know what the next block will be.

why not? Miners are looking for transactions to verify. If you have the money, and if you craft your transaction so that miners put you first in the queue, you will be quarantined to be in the verified chain.

In theory could this be done by DoSing people while mining?