Hello! It's really annoying when they nest somewhere inaccessible! I've had a few syrians now - the first was a learning curve until I found what worked. I tried the thing of deep substrate so they could build tunnels and had the same issue you're having. Stinky mess - even the hamster wasn't happy with it.
What I found was - although hamsters vary in whether they are diggers or not - they tend to only dig burrows and tunnels when they don't have a big house. When you give them a big house, that is nice and dark inside, with a litter tray inside - that mimics an underground burrow and they are happy in there, build a big nest and use the toilet - that makes life much simpler - you then just empty the litter tray once or twice a week and the rest of the cage stays clean and dry - with that method I go about 3 months before changing the substrate (keeps the hamster happy too) and just spot clean the odd handful out now and then and add a new handful. Any other items, like the wheel or any toys can be cleaned as and when. It is much better to do "partial" cleans and not clean everything at the same time as then something always smells familiar and they are less stressed.
Anyway back to housing. Your hamster has chosen to nest under the burrow box because it's nice and dark.
So my suggestion is - put a nice big house in. Put a bendy stick bridge tunnel over the entrance so it's dark inside. Put a corner litter tray inside the house at the back/end nearest the entrance (they choose the end furthest away from the entrance to nest as it's darker).
A shoebox house is ideal. Cut the base out so it's open underneath and sits directly on top of the substrate (so they can bury hoards under the nest and have normal behaviours like that). Keep the lid as a lift off roof (easy to get the litter tray out without disturbing the nest). Cut a hole for a door - ideally at one end of one of the long sides so the other end is darker.
The flat roof also doubles up as a platform to put a food dish on eg. And the bendy stick tunnel entrance doubles up as a ramp onto the roof.
This works for me every time
The tunnel entrance tempts them to move in (they head for the dark) - there is enough space for them to build an enormous nest and their natural instinct is to pee away from the nest - they will use the litter tray.
You probably won't have space for that and the digging box so I would remove the digging box, spot clean the pee a bit and then pop the new house over the topof where the digging box was.
It's always best to leave their nest and hoards if you can - they get very precious about those and as Ria says they can start peeing on the hoard if you keep removing it. I leave it till I do a substrate change. Dry food hoarded keeps fine. Unless it's pee'd on, then you have to remove it but try and leave a dry bit behind and always add new food in the same place, to replace some of the hoard.
They actually eat from their hoards mostly. The food in the bowl is usually just pouched and then hoarded and they snack in bed
Makes it nice and easy for both of you. Easy for you to get at the litter tray so it doesn't get too stinky. Easy for the hamster to find a cosy dark place to nest and easy for them to get in and out of.
I find usually if they have a big dark house, they don't bother to dig tunnels. There has been the odd "digger" exception. Who nested UNDER the house! If yours does that then just keep minimal substrate under the house and part bury it (so just the top half is sticking out of the substrate) - then they can't disappear too far down inside the house - if that makes sense.