If it’s only for recording would a plug in or dirt on another track which could be blended be a work around rather than doing it all in your signal chain? The beauty of recording is the flexibility it offers. Might be a faff but if your taking a clean di and your pedal board sound in theory it should be a simple enough.
The other suggestion might be adding in a loop or blend and you can introduce the dirt where it works best. I have a cab sim pedal At the end of my chain and run my main dirt after the preamp and into that before hitting the desk as it makes the drive sound more pleasing. My always on dirt is in the fx loop of the Basswitch so that helps with signal chain and routing. Adding in another loop/blend might not be what you’re after but it could solve the problem?