Ok, this was an idea I had earlier today. Not sure if it would work or how well it would work, but I thought I'd throw it out there. There is a 3.7V 1600mAh battery for the DS Lite, and two of them stacked together are about the same width as a Slim battery.
http://www.nintendo-shop.co.uk/index.php?c=acc&n=560800&i=B000VO6W5M&x=Nintendo_DS_LITE_Replacement_Battery_Double_Capacity_1600mAhIf you took two of them, you might be able to remove their cases, glue them together and solder them into parallel, and put them in the battery slot of the PSP. I'm not sure if they could fit together inside an empty Slim battery shell, but it would be nice if they did. This would make a 3.7V 3200mAH battery with about 2.6x the capacity of a regular Slim battery, and 1.7x that of a Phat battery (If they are soldered in series, you'd get a 7.4V 1600mAh battery--not what you'd want)
Also, two more of these batteries would fit easily into an empty UMD slot (where a CR-3100 would normally go). With a total of four of these batteries, you'd have 6400 mAh--a little over 5.3x as much capacity as the original Slim battery, or 3.5x that of a Phat battery. Not necessarily 5.3x/3.5x in battery life, but in capacity. Your battery life would increase, but I'm not sure by how much.
Like I said, I haven't actually tested this, it was just an idea I had earlier today.
