Maybe I'm missing something here: could you assign the less-visually-critical Grid view to your less-good monitor? Then you could both Loupe view and use Develop, along with their menus, on the better monitor. That's where you ideally want to see the detailed results of your editing, and keeping menus on the  same screen seems logical for that (less chance of getting Wimbledon Neck).

Management would maybe work better with grid and palettes brought back together, so you can switch functions over temporarily as needed - e.g. with G, E, shift+G and shift+E. The Shift modifier sets what happens on the second display - AFAICT when one is set to Grid, if the other one is already Grid then that is bumped to Loupe - and vice versa.

I do see how you might want to move tool panels to a different screen, for the best view of your picture - but at the same time, I don't see how you can comfortably do so all the time, because this means bouncing your attention from one screen to the other - the critical editing involves both the image and the sliders together. That was why I suggested keeping Grid view available: it's rather a distinct mode of working in any case. Many things you do there can be done off keystrokes, using icon badges, right-click context menus and so on. I suspect every single LR user has a unique combination of things they like to do with keystrokes, vs things they like to do with the mouse. We work best when the tools are comfortable to us, IMO.

So Tab and Shift+Tab give you instant room to work on your primary (or single) screen, but - importantly - without breaking the chain of thought. My hesitation about jumping the interface back and forth between screens, is that we shouldn't be really thinking much about the interface, we should have our attention on the pictures.

Using loupe info overlay can remove some need to refer to metadata panels, also there's a handy little info summary under the histogram. Once you have some view filter presets saved, some export presets saved, recently accessed collections in the list, and so on... the need to constantly go out of and back to the Develop-window-plus-filmstrip does reduce. Thumbnail badges are great - clicking them takes you to the control involved, and you can manage stacking etc nicely that way.