I have compiled a lot of info here...
Most of it can be found @ http://www.turbo-mopar.com
The OBX is actually designed for a Neon or Avenger/2GNT Eclipse with a 420a engine. The tranny is called a T350 which has a compatible differential to the 520/523 transmissions.
It is possible to use the OBX with the 555 but you need to swap out the ring and main gear with one from a 520 tranny from the same year (the 555 changed in '89).
This is commonly called a "hybrid transmission" and is necessary because the OBX is compatible with the 520/523 ring gear and not the 555 ring gear.
Gearing is usually changed when you do the hybrid tranny since the 555 had a 3.85 FD and most 520 trannys are 3.50. It might be just fine with a 2.4 though since you have lots of torque to spare. If you want to keep the 3.85 there are 520s that have a 3.85 FD but it still requires both the ring and main to be changed because the tooth count and pitch are different than the 555.
The OBX also uses large spline axles so you will need to change those out for the 88+ axles if you have small spline axles
My OBX is actually in a 568 with a 3.77FD from a 92 523 since it is a good comprimise. That isn't an option with the 555 unless it is an 89+ model in which case I THINK the 523 is compatible. Cliff or Chris Ramsdell would be a better person to answer that one.
If you have an 89 555 I would look into taking the 555 gears and putting them into the 523 to make a 568 out of it. The 523/568 shifts better and is overall slightly stronger than the 555 (unless a chromo end plate is installed in the 555) anyway and the only change you would need is a shifter and cables. It is more work but 555s are getting rare anyway so it might save you some hassle later on.
The OBX can be purchased on ebay and then I would recommend you buy the $32 bolt/washer kit from me. They are also available from www.turbosunleashed.com already upgraded with my kit.