Here is what I think would be a good wiring scheme based on the parts you have.
Remember you have three humbuckers, regardless of the size of the Little 59.
With a normal 5-way strat switch you have the following combinations available.
1. Bridge
2. Bridge and Middle
3. Middle
4. Middle and Neck
5. Neck
To get any other combination would require a different switch.
You have two tone controls and three pickups. Which pickups do you want the tone controls to influence? e.g. a standard strat would have no tone control for the bridge or it could be wired so one tone controls the bridge and the other the middle as in the diagram linked below. It would be simple to change as the wire to the tone pot you would just move to the corresponding hot wire lug for the respective pickup.
Back to splits...with the switch you have auto splits would not work as you would need a super switch but the splits could be achieved for the neck and bridge via the Push Pull DPDT and also the little 59 with a diagram I will link below.
1WD Music .01 Ceramic Capacitor, Ideal For Retaining Some Treble With Tone Control Rolled Off
Is this for the treble bleed if so it goes on the volume knob and would retain treble with the volume rolled off. A treble bleed using a cap is connected between the input and output lugs of the volume pot.
Here is a wiring that will work well I think with little adaptation. Ignore that they are single coil size humbuckers the wiring principles are the same. For the little 59 wire as the colours in the diagram and for the Bareknuckles map the wire colours as below compared to the SD wiring code.
Seymour Duncan Black White Red Green
Bare Knuckle Red White Green Black
The below diagram also should have the advantage that when all three pickups are split the 2 and 4 positions should be hum cancelling.