Got more pics.... a lot more pics... too many pics.... gonna bore ya - but you're getting them anyway
Took the whole unit out, hoovered up all sawdust, bits of metal, crumbs and something else that made a cool noise as it went into the hoover

... then put it all back fixing it down properly and tightening everything up fully for the first time!
I'll start with the drawers... here's a one...
... and from a different angle...
As you can see they have more screws than needed - and furniture blocks underneath too. The excessive screws were just to make sure and the block were really to help me keep things in place while I put them together (no bench and only one pair of hands!) - cant hurt being extra tough though.
Check out that drawer front!!!!! That's got 8 screws going straight through the front holding it onto the drawer!
Screwed the screws almost all the way in, cut a tiny slit in the carpet just big enough for the head, then screwed it all the way in to countersunk. Quick rub of the carpet with my thumb and the slit sealed up prefect. Never know they were there
The handles were a problem. As I suspected they were made for metal doors no thicker than a gnats forearm! Problem was that even if I could get them to clamp onto the 18mm ply (wasn't going to happen), the slam latch bolt would never reach the hole in the cross bar it was supposed to latch into.
In the end I decided to take a couple of layers off of the ply the shape of the handle to truly countersink the whole unit into the front. This gave me just enough depth so the slam bolt was sticking far enough through to reach the hole. I had to "move" my holes in the bar forward a bit - but I got there. Had to get some longer bolts for the clamps too - and stopped them collapsing when I tightened them by chucking a nut on the other side of the plate - not ideal but plenty strong enough.
Here's the back of the handle setup... oh.. I "moved" that hole in the drawer bottom too - it's centred now

...
... and a better shot of the countersunk unit... the carpet really helps to make it look neat...
Carpeted them up of course... but as I had measured everything with no margin for error (and then made lots of errors) things were obviously going to be really really tight between the fronts and the tops. Got round it with a cool little trick. Didn't want the carpet in the joint between the front and the drawer - but didn't want to cut the carpet so it was just stuck to the top with no wrap - so I took off a layer or two of ply just at the top where the drawer sides meet the front - tucked and glued the carpet into the space and hey presto - the carpet doesn't get pushed off when the drawer closes - and the joint is still tight
This is before I trimmed it all up - but you get the basic idea...