If the hollow back doesn't need to be perfect, use a Forstner bit and cut overlapping holes in it to get the desired depth.
You could also treat it like a big bandsaw box, and cut all of the sides off, and glue them back together. The glue line on a clean cut with the grain is hardly noticeable. You could also just build a new mantle as a hollow box and ...
I am assuming by CNC machine, you mean a router.
The blue line section that is horizontal will be a regular 90 degree cut. The sections of the blue line that are on the curves will have an increasing large fillet as it approaches the bottom of the cut, unless you have a 4th axis on your CNC to rotate the item. The cuts on the curves will also not be ...
My guess is that you do not, in fact, have a flush cut bit, but rather a hinge mortising bit, such as the Freud 16-560, that is designed for templates that are slightly oversized.
You can either get a proper flush trim bit, get a different bearing for the bit to make it cut flush, or modify your template to account for the offset.
The depth that a router can cut depends on the router as well as the bit. Look for a long router bit and you should be able to cut to the depth you need. You don't need a large bit - use a small (3/8 or 1/2" diameter) bit and multiple passes to cut the groove.
We have a live edge table with a lot of the flat part of the table being some 2 inches in from the bottom of the live edge. Several times this has caused things to fall off the table, as it keeps people from sitting closer.
This is an extreme case.
As a kid we had a table with an ogee edge. That edge was narrow enough that it was easy to nick.
My take: ...
As a one-off, my first hunch was to lop off big chunks with a hand saw, then go at it with a spokeshave. It looks like most of it can be done reasonably along grain-lines.
If you know the radius, make a 1/4-round sanding block (sandpaper plane) by either making a radiused router sled or cutting something on a table saw with an appropriate-sized blade (6 ...
I'd use a handheld circular saw.
Clamp the workpiece securely. Plunge at one end, run full depth all the way along. Stop before the end. Repeat, on ~1/2" spacing. Clean out the mess with a chisel.
You won't get 4" (unless you find a saw with a 10" blade), but you should get a decent enough depth for cords.
** When plunging, do not be tempted to drag the ...
Found these bits on Amazon
Little bit odd with all the flutes but I think it'll do just fine at least in the short run.
You want a 45 degree inverted chamfer bit.
Many of these will have a bearing on the bottom - this will be removable, but there might still be a nub that keeps it from cutting flush. Maybe you could grind it off?
I don't think it makes much difference. If you have a smaller cutter you can move the cutter faster; if you have a larger cutter you will have to move it slower. The limiting factor is how fast the motor can cut wood.
Obviously if you use an extremely thin cutter your CNC machine won't be able to move fast enough, and if you use an extremely large cutter ...
Commercially this type of deep profile will often be created using a spindle moulder1, a floor-standing machine sort of like a router table on steroids.
But no small-scale professional woodshop or home woodworker would approach this as a single operation. Instead the profile would be broken up into portions that can be formed by separate shaping operations ...
My Makita 3709 has only one collet and the instructions booklet say that it's valid both for 6mm AND 1/4" bits.
Clearly, if the collet fits 1/4" it can also fit 6mm, probably by just a tiny extra tightening.