Some travel agencies will courier your passport to Hong Kong but that's just going to add to your costs. You will probably need to go through Hong Kong anyway if you are heading to China from Taiwan so your best bet is to pick up your visa there. HK is generally the easiest place to get the China visa, I got mine within 24hours. It's worth keeping in mind however that current policy is to insist on an onward ticket and confirmed hotel bookings before the visa is issued.