It seems most of the backlash around that was due to you suggesting you publish IP addresses. Since you are already taking credit card details I don't think people would object to recording IP addresses to prevent credit card fraud (maybe only record IP addresses for credit card transactions not general usage of the site). If someone wants to anonymously contribute they already have to get an anonymous credit card, getting around an IP address block would seem trivial.
I would also, advise against your plan to just white list givers. There are already too many barriers to contributing. I would suggest just charging and holding onto money when the transactions seem dubious. Do you also get charged the cost of fraud? because if you don't I would just charge the credit cards and forget about it and let your provider do their job.