[T]here is a case for capital punishment inflating the death toll even when not counting the capital punishment itself. If you face a likely death penalty, there is no incentive for you to not kill others. Killing others, like witnesses, can then be rationalized by it reducing the risk of getting caught, and thus die.
This resembles the argument that were we to make rape, for example, a capital crime, we should only be aiding the rapist to reach the decision whether "merely" to rape his victim, or to kill her into the bargain. (The gendered language I here employ, if it be 'sexist,' is by no means casual.)
You may well be correct especially in the case of criminal organisations inclined towards rational, albeit ruthless, calculation. Generally however, arguments based upon deterrent and incentive, as they pertain to the ordinary felon one imagines inhabiting death row, need IMO, to be approached with some caution.
In the first place, there being little to prefer in a life-long custodial sentence, capital punishment per se may not add too great a store of incentive to deal mercilessly with those whose knowledge might betray the original crime. Instead this problem may be one born of draconian punishment generally. Where there exists no chance of redemption, one will not be motivated to redeem oneself.
Secondly, --and this applies more properly to those arguments which, in ignorance to the insight you provide, regard the threat execution as providing a greater disincentive, --I think it an error to imagine that ordinary felon as a rational maximiser of utility. Choosing between two situations, one in which murderers instinctively covers their tracks by the commission of further crimes; and one in which they calmly determine the scale of their offending in consideration the probable sentencing outcomes, I find the former by far the more likely.