So if we buy 8-day parkhoppers from GAT for $204 (so that we can get Saturday), and then upgrade to APs on Sunday, what is the cost? Is it $259 (cost of AP) - $204? or $259 - $239 (cost of most expensive 5-day parkhopper from Disney)? or something else? Does Disney know what I pay GAT?

Figured I'd answer "out loud" as well as replying to your PM.
The price you paid is encoded in the ticket, if not printed directly on it. Our hoppers from Costco Travel didn't have the price on them, but the AP people could see it on their computer, and they knew just what to charge me.
As I mentioned in the PM, this is one way DLR differs from WDW. At WDW once you use the hopper, the new price is somehow put onto that ticket, so if you upgrade, you keep whatever discount you had. But with DLR that doesn't happen. You'll always end up paying the current price of the AP, at the time you upgrade, so unless you really need the "layaway" option, where you're saving money up over time, there's no need to get discounted tickets, as the total will be the same.
There's even a problem that was re-mentioned here recently, when people think about upgrading from specially discounted military tickets, where you'd end up paying MORE than the AP cost, b/c you are paying the more for the hoppers than is encoded on the ticket. So you pay 150 when the ticket is encoded with 140, and now you have to pay a total of 269 instead of 259! But that doesn't impact you, I'm just chatting.
If you're going to upgrade immediately, just know you won't get both MMs of the GAT tickets. As soon as you upgrade, you lose the MMs from the ticket.

But if you're staying onsite, that doesn't matter, b/c you get it from the hotel (unadvertised perk).
Since you're planning on spending the money to upgrade, and planning on upgrading before using the 2nd MM from GAT, I personally would just buy from
disneyland.com. Buying from them, you print out the voucher and take that voucher straight to the GATES, not the ticket booths like with GAT, where the voucher is turned into a ticket.