OK, so I think I see the difficulty. I think the prohibitions tables in ACBC call for exact matches, so the missing attribute levels when you have different numbers of attributes showing for different respondents causes problems.
How common is it for the summed price to come back zero? Remember, there needs to be a random shock to the summed price values, or you cannot partial out the effect of price (obtain a separate utility estimate for price) without that.
If it is only a rare case that the price comes back zero, then perhaps you ignore that. Or, perhaps you can set up your pricing tables and the %shock up and down from the summed prices such that obtaining a zero price was not logically possible?