A quick
ITA Matrix search (from YVR, to all airports within 2K miles from STL, ua*, in October) shows availability most days at C$270 RT for YVR-LAX. ITA Matrix is very powerful for this sort of thing; put in the cities you'd like to try, click "Advanced Routing Codes", and put ua* in the routing code boxes -- that'll give you all flights with UA codes. o:ua* will give you flights operated by UA, potentially with other codes (e.g., AC).