Berryman B-12 Fuel Injector Cleaner (part #0116 or Part #0101) is ideal for that task.  The product needs to come in contact with the gum/varnish as completely as possible in order to keep the soak times reasonable.
You’ll need to use enough 0101/0116 to cover the entire affected area and ideally, be able slosh it around in the tank a little in order to make sure you get all the low areas well but also a bit up the sides.  If you can do this by rocking the vehicle, great.  If not, you might consider taking the tank off.
You should try to leave the cleaner in the tank for 2-3 hours, moving it around occasionally, before draining it.  Please note that it might require a couple applications if you have a lot of gum/varnish in the bottom of the tank.
Don't heat the product up above about 90-100°F.