You will hate yourself if you do stack up number two ;) Maybe that's harsh but it's a going to be a PITA reworking a board with all internal signals. Don't be afraid of vias either.
Let's address some of your questions:
1.Signal layers are adjacent to ground planes.
Stop thinking about ground planes, and think more about reference planes. A signal running over a reference plane, whose voltage happens to be at VCC will still return over that reference plane. So the argument that somehow having your signal run over GND and not VCC is better is basically invalid.
2.Signal layers are tightly coupled (close) to their adjacent planes.
See number one I think the misunderstanding about only GND planes offering a return path leads to this misconception. What you want to do is keep your signals close to their reference planes, and at a constant correct impedance...
3.The ground planes can act as shields for the inner signal layers. (I think this requires stitching ??)
Yeah you could try to make a cage like this I guess, for your board you'll get better results keeping your trace to plane height as low as possible.
4.Multiple ground planes lower the ground (reference plane) impedance of the board and reduce the common-mode radiation. (don't really understand this one)
I think you've taken this to mean the more gnd planes I have the better, which is not really the case. This sounds like a broken rule of thumb to me.
My recommendation for your board based only on what you've told me is to do the following:
Signal Layer
(thin maybe 4-5mil FR4)
GND
(main FR-4 thickness, maybe 52 mil more or less depending on your final thickness)
VCC
(thin maybe 4-5mil FR4)
Signal Layer
Make sure you decouple properly.
Then if you really want to get into this go to amazon and buy either Dr Johnson's Highspeed digital design a handbook of black magic, or maybe Eric Bogatin's Signal and Power integrity Simplified. Read it love, live it :) Their websites have great information as well.
Good Luck!
Do you have any unplated holes or slots in the PCB's? I've previously specified some unplated holes on a similar layer stack, and found that the supposedly unplated holes were in fact plated and the plating was creating a short between the power and ground planes. A round file and a few minutes work quickly sorted the problem out.
Best Answer
The problem is indeed with the crossing 1-15 and 2-16 vias. The manufacturer has to be physically able to make the board. There may be a way to attempt that construction, depending on the equipment the manufacturer has.
There are two straightforward ways to get close to what you have drawn.
1) 1-2 core, drill, thru plate. 15-16 core, drill, thru plate. Assemble, drill, thru plate. That gives 1-2, 15-16, 1-16, but not 1-15 or 2-16
2) 1-2 core, drill, plate. Prepreg 15 foil, drill, plate, prepreg 16 foil, drill, plate. That gives you 1-2, 1-15, 1-16, but not 2-16 or 15-16
More expensive, but I have used the process, micro-vias. It's mainly used for their small footprint, to get tracks between BGA balls.
3) As for (2) but with a final micro-via step which is laser drilling 15-16, power set to ablate the prepreg, but stop at the 15 foil. These vias would be very small and fragile, pads connected to them do not generally survive rework.
4) Speculative. The micro-via process only works because of the small thickness 15-16. It may be possible to micro-via from 16 through to 2, via an aperture etched in 15. Ask the manufacturer. They may have the capability. If you wave money at them, they may be able to develop the capability for you.
5) Speculative. You could replace the 2-16 via with 2-15 and 15-16 micro-vias, if the board vendor was happy to insert another micro-via step in the (3) buildup above.
It would be far better to think harder about your layout, and try to use the standard routes.
Do note that your board construction is unbalanced through the Z direction, this is strongly discouraged by most board vendors. It will probably warp after exposure to soldering heat, cracking your ceramic caps.