We stayed one night in Imabari before completing the Shimanami Kaido and I researched transporting luggage between Imabari and Onomichi (I lived in Imabari for 2 years so am familiar with the area) before we left and the information all suggested that we could get luggage transferred from our hotel in Imabari to a hotel on the transfer list in Onomichi even without a booking.
However at our hotel in Imabari (with no English speaking staff; I had to rely on my limited Japanese) we tried to arrange for our luggage to be transported to our next hotel (in Kurashiki, one hour north of Onomichi) but despite my previous research, we were informed that we could not get it delivered on the one-day service to Kurashiki, and it could ONLY be transferred to Onomichi, and ONLY to a hotel on their list. As we didn't have a booking in Onomichi we tried unsuccessfully to get the staff to arrange an alternative for us. While the lady at the front desk went out of her way to help us, this couldn't be arranged and we booked the Royal Hotel just to get our luggage delivered. We didn't end up staying here, but from what we saw from the reception, it is very dated and has a smoking room by the front entrance. For budget travellers only! I give this advice to anyone wanting to arrange hotels in Imabari/Onomichi, who want to do the bike ride and get luggage transferred...