I currently have two merchant accounts and an account with
2Checkout.com and CCBill.com

Some of my websites have recently come under attack by stolen credit
card thieves. I need to find a transaction processor similar to
CCBill.com that actually calls "suspicious" transactions to verify the
charges. I need to find a service that will either call the bank or
the customer themselves. Please provide a list of possibilities. I
would like to find a service that includes everything, transaction
processing (credit card + online check) as well as the verification
process of insuring the transaction is legitimate.

USMS provide both merchant accounts and gateways including
AuthorizeNet, IntelliPay, Optimal Payment etc. Yes the service can
check "suspicious" transaction using AVS "Address Verification
Service", and monitor your monthly volume as well as average ticket
size. The service will hold your transaction if activity is outside
your normal range. You can add service to accept online check. Please
email to bessh@usms.com for additional info how to setup.

http://www.whylabs.com/

WhyLabs aims to protect your assets against online fraudulent attacks
using the most advanced and secure technologies.

Geo Location matching, BIN analysis, Email address existence, Distance
calculation (IP, Billing, Shipping), Black lists (IPs, emails, credit
card numbers, phone numbers), Phone number analysis, List of high-risk
countries and regions, Proxy server detection (incl. non-standard TCP
ports), Free email domain checking, Similar transactions analysis
system.

These guys will do what you need without haveing to change your processor :-)

If you don't mind saying Paul @ Smiths Media Solutions UK sent you
that I would be very greatful :-)