I know you said you deal with 5 different companies for shipping but have you tried using something automated to see how close it would be? Maybe you could find some way of getting a close price where you don't over charge by too much but you can give a price to someone who wants to know the price but is not willing to wait for a reply. Or, if possible, get a price from all 5 shippers and list them all and let the customer choose.
I'm the type of person who just wants to know what it will cost me so I can decide if I really want it or not. Often times I ask businesses what it will cost to ship something and they take their time or just not even bother. I've even had one place tell me that I would have to deal with all the shipping from my end (somehow I would have to guess weight and size for shipping and would know what they have for loading the truck).