It's not blocking anything; the trainer works now that I've temporarily disconnected my second monitor, but even though the infinite health cheat does work in the main game it doesn't work in Not a Hero. All of the other cheats work in Not a Hero, though.
I figured there was a system like that, and that's fair; I only mentioned Not a Hero and not the other DLC that came out recently (which I haven't tried the trainer with yet) because Not a Hero is free, so there's no need to buy it. I can live with the rest of the options that do work with it already, I just wasn't sure if they were all supposed to or not.
Edit: Also, just for the record, I've tried it out now and the infinite health code does work on the new paid DLC, so Not a Hero seems to be the only thing it doesn't work in.
[Edited by Jocosity, 12/13/2017 4:04:10 PM]
The unfortunate thing is that savegames are not exchangeable for this game so we cannot reproduce your issue as we have to play the game for as long as it takes to get to those areas you describe here.
As you already found out which trainer option is causing this... thanks for sharing!