Zack Black

Ah, got it! Thank you so much for showing me how to do this - I really appreciate it. Definitely more awkward than just having the marquee snap to the grid but at least I can work with this. I truly hope the developers take note of this and update the functionality soon.

Snapping works for me for post-selection even on the same layer. Check your snapping panel so that "Snap to grid" is actually enabled. Click the down arrow next to the magnet to check the settings.

There may be a faster way than I could think of, but this isn't a workflow I follow anymore (I do my spritesheets in Designer with Artboards now). Anyway, you could set a keyboard shortcut (see below) for Select>Reselect after your first selection, use V&Q to move it where you need it again and make that selection more mobile that way. That is if you can get your snapping to work. So that way you're only really transforming the selection box once and basically panning around the canvas doing copy and paste operations.
I'm not real sure why we can't just set Marquee to snap to grid. Maybe we can and I just haven't figured it out for myself. I do agree that would be quicker.

Edit: Even better yet, maybe create a Macro for the Select>Reselect (no keyboard shortcut necessary), V, Q operations.. that way you can just pan your canvas as needed with your 8x8 block with one click. Not ideal, but an adaptation centered around your method.

I humbly suggest to rewrite your post a bit up top so that it can easily be read by staff (who does read) that you are requesting the ability to snap marquee tool to grid without Quick Mask (Q).

Click outside the selection (in the red zone) and it will leave the mask with the selection.
If you are using the Background Layer (basically if you opened an image as-is), you must unlock it to be able to shift pixels around. (The lock has to do with blocking movement, not edits) (Sorry I assumed you may have figured this out)
FWIW, I use ScreenToGif if you want to screen what's actually happening on your end (in the future). A simple but powerful little app.
https://www.screentogif.com/

Seconded! Would love this feature.

The Rectangular marquee tool (in the Selections persona) should:
 
snap to grid, guides and layers AND corners should be points one can select and move to resize (and snap to grid/guide/layers)  
Ex: Its a feature from Pixelmator that i miss a lot.
 
 

Totally agree with all the above comments. I have just started using Affinity instead of Photoshop (which I have been using for years). The missing snapping feature for the rectangular marquee tool is making it impossible for me to continue using Affinity...

Absolutely. It's this feature alone that's stopping me using the program. It's quite a basic feature and I'm surprised it isn't there.