This is the potty litter tray I mentioned. Size is just right for a syrian. Ours tend to pee in the very back corner and then sit for a wash in the front. They are quite clean tidy little things if they have an ensuite bathroom! Chinchilla sand is better than potty granules (which aren't safe if eaten although none of ours ate any). If you're not in the Uk,Amazon.com sells similar ones but check the size carefully - this size is good but some are huge for guinea pigs.
https://www.amazon.co.uk/Trixie-Corn...0710684&sr=8-7
If the house isn't large enough for a litter tray they will often choose a corner of the cage as a toilet so you can put the litter tray there. The trick is to put it where they choose to pee or they will ignore it. For me I have found it works every time to put it in a large house.
The reason for avoiding too much cleanouts isn't just to save you the hassle - it's because it really stresses the hamster. It removes all their familiar scent. They scent mark everything in their cages and leave scent trails and routes as well. This is partly to "mark" it as theirs but also to help find their way around the cage easily as they don't see well at all.
If the whole lot is cleaned at once they are lost and it doesn't smell familiar any more so it really does stress them. With a litter tray and spot cleaning you don't need to change the substrate nearly as often. With a large cage I go 2 to 3 months without changing the substrate, and even then I replace some of the clean old substrate on top of the new substrate - it helps them accept the clean. So the trick is - to clean things at different times, so something always smells familiar. eg wheel a different week from any toys and substrate a different week again.
Their nest and hoard are their most precious things. I always leave the nest alone. When it comes to doing a substrate change I prune the hoard if it has got too big. But dried food when hoarded lasts quite a long time so can be left unless pee'd on. If it's pee'd on and you have to remove it, but try and leave a little bit of dry hoard and then always put new food back in exactly the same place. If they feel their hoard has been "stolen" they start doing unnatural behaviours like peeing on their hoard to deter anyone from stealing it and then it's a catch 22! But can usually be resolved in time.
Likewise if the nest is pee'd on then it will need removing but again try and leave a little bit of old dry nest behind so it smells familiar, then put a big pile of new paper nesting material out again and they'll rebuild it. I keep topping up the paper pile regularly as they can build really big nests in winter to keep warm so if it gradually goes down, keep topping it up.
You can just leave the nest otherwise - it stays clean and dry and they refurbish it themselves - often chucking out a bit of nest and bringing new nesting material in.
Our first hamster actually used to clean out his own house! I would wake up and find a big gap in the middle of the cage with no substrate, and a big pile of whiffy substrate in front of the cage door. He had removed all the whiffy stuff for me to take away and dragged in a load of clean from the middle of the cage.
They need something to do!