"Ofmega cranks, including those branded "Avocet" use a non-standard spindle, thinner than either J.I.S. or ISO spindles. As far as I know, nothing else works". Sheldon Brown's Bottom Bracket Size Database

I believe all the Ofmega cranks/BB have the Ofmega propitiatory square taper, (I will update velobase). As mentioned earlier there is no point switching to a different BB as it will still need to be Italian. As mentioned the only way to properly tighten the fixed cup of an Italian BB is with a BB tool Amazon.com : Park Tool HCW-4 Box End and Pin Spanner Crank Wrench (36mm) : Bike Cranksets And Accessories : Sports & Outdoors and $17.40 would certainly be a good investment.

If you must get a cartridge style BB you will need to switch the crankset also..