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I'm guessing about 7 mods. There's factorization for the barrels; the clipboard may be from dartcraft (the one in the story looks like it is used to store information but maybe Craig was testing to see if the materials crafted correctly?); the building is probably made from MFR whitestone...
Have you tried setting all the tesseracts to ignore redstone? Maybe there is something at the quarry that is shutting down one of the tesseracts sometimes.
You should be able to do it that way, just make sure you've got the 1.4.7 version (which might not have the wrench) because FTB is still on 1.4.7. Also, all the packs are still being updated but they are waiting for 1.6 for that.
I think it puts the waypoints at equivalent positions so if you build a portal at one it should come out at the other (assuming there is space for the portal).
You could see if the tool I linked works. That changes the ids of the blocks in the world so you don't need to adjust your configs which might be better for a server.
EDIT: Of course, this will be time consuming too but you only have to do it once.
This might help (though of course you will need to make your own patch.txt going from the tekkit lite ids to the ftb ids). There are a few things that tekkit lite has that ftb doesn't so you will probably need to map them to stone or something.
You could probably attach the interface to automatic crafting tables (mark 1 or 2), liquicrafter and the cyclic assembler as well (though I haven't tried all of those).