An advantage of a local power plane is that you can leave all the power routing out of your signal layers and in stead focus on the coupling, routing and impedance control of your signals.
Other than that the best advice is always based on your complete and exact design, so I'll tell you some of my preferences and their reasons, and leave them for you to consider.
For reasons of know-variables I prefer to keep no other layers between the GND and important signals, so in complex designs I try to make as many Signal layers directly next to a ground that fits my stack-budget (of course I'm not spending the money for 16 layers on each design I make!). And if I can only get 1 reliable layer like that, I make sure that layer has only signals and hosts at least the signals that are most important or highest frequency.
For the distances of the stack-up you best call the fab you are having the PCB made at, they know what they can do and what they stock. Once you have those numbers you can use them for your impedance control if you need to.
They can also tell you how accurate their PrePreg procedure is. If it's not very accurate or the layer it is spread on has a lot of copper areas and a lot of gaps as well (this makes PrePreg harder to get uniform) sometimes you will want your Signal and GND on either side of a normal plate, to be able to perform good impedance control. If that is a demand you might want to go for your first choice, but swap the "SIG" and "Sig/Pwr/Gnd" layers.
Another thing you put in your title is Analogue, if you have high-fidelity requirements of analogue signals you are not going to regret splitting your Analogue and Digital power domains completely, including the ground planes and only connecting them at the power-input of your board. You'll be thanking yourself for the extra effort once you find you measure very little digital noise in your analogue signals.
Your best bet would be to create a new clearance rule (Design -> Rules -> right-click "Clearance" in the left pane, select "New Rule", open up the new rule you just created (it'll be titled "Clearance_X" where 'X' is the highest number you see) and in the section labeled "Where The First Object Matches", open the dropdown and select "Net". A new dropdown will appear, and you just need to select your RF Antenna net from the list. Then set the clearance in the "Constraints" section. This will apply this clearance rule to your RF antenna net only, and this will ensure that the polygon, components, and other traces are pulled back from this track. Keep in mind you will probably need to repour your polygon after setting the rule (Go to Tools -> Polygon Pours -> Repour All, or shortcut T-G-A).
Best Answer
I've been told to post my comment as an answer, so here goes.
While eMMC does have a lot of balls, most of them are NC, and usually are safe for routing signals through the pads.
So, if you can route signals through the NC pads, you don't really need fancy vias or thin traces you'd normally need with 0.5mm BGA. You just get the traces going through the pads. The standard pin set up allows you to route the whole thing on a single layer then.