Recently I began experimenting with using buildcraft or Redstone power piping to interact with reactors. It does work sorta ok because the reactor has an inventory just like a chest. However, there are a couple of things that the current implementation does wrong :
Buildcraft/Redstone Power cannot access anything but the top row most of the time because you actually leave the entire inventory grid open even for a 4 chamber reactor. Instead, whenever an item gets inserted where it is not allowed, it gets ejected. Since Buildcraft/Redstone Power fill a chest row by row, they cannot insert into the right-most slot in the top row for a reactor with less than 6 chambers because the item gets rejected.
I have managed to get items into the next row from the top by inserting items extremely fast via pipes such that say 10 buckets enter the reactor in 1 tick, before the reactor gets a chance to eject anything, and so the items in valid slots stay.
Fix for this : fill the extra slots not in use with a spacer item. (say the "fire" block) If the reactor is destroyed or wrenched, make sure that the code that causes all the contents to drop exclude this spacer item. Simple, and reactors would interact properly with buildcraft/Redstone Power.
This bug is on your end, not these other mods because those mods are working correctly - your mod is just exposing slots that are not actually valid destinations. Another fix for this would be to change the inventory registration for Forge.
It would also be nice if the side blocks could have their inventories accessed by mods, but this is a lesser consideration. It actually adds a balancing element in reactor design in that you can't connect a 6 chamber reactor to pipes.