So far my way of payment has been a part before and the rest afterwards depending on what we shot. I think th cc payment is a good way if you don't know the client well enough but as earlier said the cost is on you so include it in the price.
When talking to people about hunting in Africa everybody is afraid of all the extra costs that might appear. This would be just that extra cost they don't like. Though I don't think anyone (not many at least) bother if the trophy price for a kudu is 890 USD or 930 USD for example.

Also it might be good to have a backup plan if the cc won't work, that can happen even in the most modern enviroments!