If you're just starting for the day, or are coming back from the island, your shortcuts are a clean slate. Your position in the queue at this point is situated between the first and last tools in your inventory, so pushing right pulls out your first tool, and pushing left pulls out your last tool.
As soon as you have a tool in your hand, either via shortcuts or inventory selection, that tool is your current anchor, and when put away, is selected no matter which direction you push. YOUR QUEUE IS ALSO ESTABLISHED AT THIS POINT. The game loads up your queue relative to how you have your inventory arranged at this moment, and no matter how you arrange your tools after that point, the queue will be unaffected. It does this to avoid situations where you're switching tools to catch bugs and fish and dig fossils all at once, which jumbles up everything in your inventory. Even if everything is jumbled in this manner, your queue remains unaffected.
MANUALLY REARRANGING THINGS IN YOUR INVENTORY DOES NOT ALTER THE QUEUE. Once your queue has been set, the only thing you can change is your current anchor. You can, however, clear out the queue and start again. As far as I know, the only queue clearing events are going to or from the island and saving/restarting. There may be others, but I haven't noticed them yet. It certainly wouldn't be hard to test, if you were so inclined.
So, the easiest way to manage your shortcuts is to NOT OVERTHINK IT. At the start of your day, line up your tools in the order you want them, and just simply don't mess with them. It's as easy as that. And just make sure your tools are lined up how you want them at the end of your day and boom, you're ready to go for tomorrow.
My tools go shovel > can > megaphone > slingshot > rod > net. My two most used "on the fly" tools are at the ends of the cycle, ensuring they're always right on hand. Going further into the middle of the cycle, you see my situational tools. I don't use them very often, so they're out of the way of both directions through my queue. Whenever I go to put away my held tool, I cycle back to either the shovel or the net, depending on which one I started with (usually the net, since having it immediately on hand for bug sightings is nice) and put it away, ensuring I don't get confused as to where I am in my queue. And after understanding how the system works, I've NEVER had any problems with it.
MANUALLY REARRANGING THINGS IN YOUR INVENTORY DOES NOT ALTER THE QUEUE.
Actually, I'm trying it out and it works fine. You can have your last-used tool out, go into inv, rearrange things and it'll cycle through in that order. I also found something interesting: When you press down to put an item away, it actually saves the slot the item's going into as the go-to for the next time you press left or right. So lets say you have your shovel out. Put the shovel away with down, go into your bag, put an axe in the slot the shovels in, then go out and press left. It will pull up the axe. This is why I was making the mistake initially, (idk if you saw cause it was in the pre-edited post) of thinking Left or right on dpad pulled out whatever was in the first slot. At this point, the mechanic is so convoluted you'd think it would've been way easier to design it, yknow, simpler...