I gigged with a BF Vibrolux Reverb for many years and I'll agree that once that old Fender tone gets locked in your head, it's hard to not only shake it but dupe it with other amps.
When I'm shooting for that vibe with my III (also an EV-loaded and EQ-equipped combo, mine's a green stripe and I run a Celestion-loaded Thiele under it), I use single coils and run this setting
volume on "6" bright not pulled,
treble on "7" shift pulled out,
bass on "4" shift pulled out,
mid on "4",
master at "2" or a little more (use the power switch on the back to control the "ouch" factor LOL), deep pulled out,
lead gain "6" to "8" depending on the howl factor I'm looking for
lead master set to match the clean volume, bright pushed in at volumes above 1.5
presence on "4"
reverb on "3"
My EQ is set at about 90 percent on the bass slider, midway on the bass/mid one, 25-30 percent on the middle one, probably 60 percent on the mid/high one and about 70 percent on the high slider.
Be ready to use the volume knob on the guitar - a slight roll down can drastically change the gain and attack of the tone, especially if you're using hot or overwound singles.
With these settings, I get nice tones on all three channels and when I use the guitar volume, it's like going to six channels.