I have a somewhat similar system and bioshock runs totally fine here (still using v.1.0).
sys specs: AMD Athlon 64 X2 4200+ (dual core, 2.21GHz), 2GiB RAM, GF 7800GT, WinXP Prof SP2.

I never heard of tsc synchronizing tool. I'm using the official amd_dc_opt.exe instead to fix dual core problems. Maybe that's the reason why it's not working for you correctly?

[edit] just realized what you mean with "tsc sync tool". So i guess you already have the official fix installed.