fb132 -
The reason lump sum investing is on average better than dollar cost averaging, is because you put your money to work sooner, thus giving it more time to compound. The market goes up over time, so waiting to invest generally means you pay a higher price. If you don't have the lump sum today, you are not dollar-cost-averaging. You are simply investing money as it becomes available. "Saving up" so that you have a lump sum to invest should, on average under perform investing your money as soon as you have it, for the same reason - you are delaying the investment, so it will have less time to compound.
That is, absent high transaction costs, but you've said you don't have any transaction costs to speak of.