A very good point was raised about Square here, which is that you cannot integrate it into your system, even for batch processing. That would mean that you would have to enter every single credit card number each month manually for each transaction and the exact amount. There is a ton of room for human error here.
I would start by looking at your verification process. Why arey ou getting so many fraud / chargebacks? Many providers ask for government issued photo ID and even call the customer to verify they are who they say they are, especaily on these types of high dollar orders. We sell dedicated servers too and our chargebacks and fraud levels are very low, because we screen everything and are very rigid with our process. If we even have an inkling that something is not right, we will just not accept the order.
I might start a thread on order verification actually, could be interesting to see what everyone here does with thier orders.
Hope this helps.