The best thing you could do would be to get you either one of the older version Six-Axis PS3 controllers, before Rumble, as it uses the Potentiometer style Sticks, or, if you're wanting to have that Rumble feature, get one of the newest versions (the Asuka or VX6) as they have gone back to the POT style Sticks.
If you're stuck with using one of the board versions with the Hall Sensors, you can try bypassing the converter IC and just go straight to the MCU with you 3DS Slider X and Y lines. I haven't tried this personally, but the theory is sound.
On the versions of the PS3 controllers that use the Hall Sensors, the MCU didn't change at all in how it works from any other version, they just went thru a phase of making the Sticks more complicated for whatever reason. So instead of POT style Stick to MCU, it goes Hall Sensor style Stick to converter IC, to MCU.
The MCU on the controller board still needs a voltage swing, like the 3DS can provide, so there's no real reason you shouldn't be able to just wire them up and use them that way after the converter IC.
You didn't specify what version of controller you're working with there, but there should be 4 TP spots after the converter IC (or ICs depending on your board version) where you can wire up the X/Y of the 3DS Slider to.
They're TP19, 20, 21 and 22 on most board versions, but again this depends on the version you have there and needs to be checked first.
Use the 2.8v source for the VCC of the Slider, same one that powers the Hall Sensors.
