350 TPs both ways sounds like 140 for TATL and 210 for direct F domestic.
you can usually built in another stop in the US for an extra 60 so try seeing if that works (though be careful with Alaska Airlines flights).
also consider going via London for another 40 TPs so something like
DUB LHR 40
LHR East-Coast 140
East-Coast - West-Coast 210
West-Coast - SEA 60