Y/M/Q/L/Z/V are all Elite/Evergreen Deluxe ticket codes for EVA Airways. China Airlines does not have Premium Economy.

You have to have an Elite/Evergreen Deluxe ticket to get into one of those seats, they do not offer Premium Economy seats to full fare Economy ticket holders.

What is late afternoon?
BR0027 leaves SFO at 18:20, operated by B744COMBI on the date you want to fly. Wonder if that fits your schedule? CAL does not have afternoon flights for SFO.
BR0011 leaves LAX at 17:30, all operated by B773ER. CI0005 leaves LAX at 15:55, operated by B744 (and you can refer to kaichun's post for the details).

Are you price sensitive? If not, EVA Elite/Evergreen Deluxe should be your choice. If you are price sensitive, unless CAL Economy price is quite cheap in comparison to EVA Economy, you should go with EVA.

By the way, just checked both sites:
It appears that all flights for China Airlines' Economy Class on August 1st are sold out... nothing to book from their website! However, you can probably try to book via telephone or through a travel agent. All other dates (before/after) are available, and the price for August 2nd would be 1109.2 all included for Economy 6 months ticket, M class. If you are interested in Dynasty Class, it would be 3669.2 all included for 1 year ticket for LAX-TPE in C Class on August 1st. Not checking SFO as it does not work with your flight time.

EVA Airways Website:
Economy 6 months ticket is 1265.2 all included for LAX-TPE on the 17:30 flight... B class.
Elite/Evergreen Deluxe 1 year ticket is 3172.2 all included for LAX-TPE on 17:30 flight... Y class (it appears that all other booking class sold for this flight).
Economy 6 months ticket is 1601.2 all included for SFO-TPE on 17:30 flight... T class.
Elite/Evergreen Deluxe 3 months ticket is 1425.2 all included for SFO-TPE on 18:20 flight... Q class.