I'm still waiting to hear back from my GM Financial rep as to how GM Financial prorates the single pay amount back in the case of a total loss on a single pay lease. The amount could possibly be prorated by months, days, miles driven or some combination. I have had that question from customers in the past so now i'm trying to get a concrete answer.
To answer your question on whether the single pay amount down is considered cash cap reduction it is not. I have calculated hundreds of leases over the last 8 years and there is a specific spot where the cash cap reduction goes. You are correct that in the case of a standard lease cash cap reduction (additional cash down) does not get recovered if the vehicle becomes a total loss. But in the case of a single-pay lease there is no cash cap reduction. The single pay is simply the sum of the payments plus up front fees.