Speculatrix: Space inside display is very limited - on both left and right sides there are PCB (display controller and power). And it will be well shielded if you close the lid.
Regarding the DS-310FS: This module may fit into both Akita and Spitz, at least into the space in the plastic cover of HDD. Antenna has to be elsewhere. You will need a special thin HF cable - either using flying wires (a bit ugly) or a small daughter board with (low profile) UM-SMA connector.
Then you need to wire one quadruble resistor under the CPU cover (see albertr's description and my photos) and then attach serial cable to pins under the HDD.
Also attach non-regulated battery/AC voltage to prevent cold start (see the spec).
Last you need to get regulated 3.3V plus its control. Regarding the control, there is free GPIO 40 and probably 10, repurpose-able BTRTS and BTCTS, several nearly ununsed GPIOs on diagnostic connector and finally several free SCOOP2/AKITAIOEXP pins. Adding a special switching IC (special transistor) will fit your needs.
Regarding the 3.3V power:
From CPU changer (step-up to 5V, then back to 3.3V, the same is wired to IOPORT): Possible, but you are limited to 50mA (and even this may shut down your CPU with a peripheral connected to IOPORT). Hopefully, removing batteries for a while returns Zaurus back.
From CF/SD step down: Surprisingly it is step-down only with attached 2.8V detector, which seems to be in contradiction with CF standard, which requires at least 3.15V for regular operation. But my CF seems to work even with lower battery. It needs to be verified, whether it is possible to keep it on, when no CF/SD is attached. (Well, I don't understand the power design here.)
From HDD step up/down changer (Spitz only): It seems to give enough power and it is bi-directional. It needs to be verified, whether it is on if HDD is down.
From a custom changer: There are even two unused changers on the PCB, intended for Mitsumi Bluetooth module. But one has to find, how they should be connected. For Spitz, there is not enough space to solder it there.
If anybody will do 3.3V power voltage research inside Zaurus, please let me know. I am searching for a solution for BT/WLAN.