I really can't stand electrics that have the acoustic-style headstocks where the tuners are on both sides

They're actually problematic as all hell! Depending on the size of the headstock, the middle two strings will enter the nut slots at too sharp of an angle and will tend to get stuck in there when you do bends, so your tuning stability will be all over the place without some mods. The only "fixes" are a String Butler (aftermarket piece of plastic with a brass rollers on it to reposition the middle four strings in line with the nut slots) or a special type of nut that has either graphite or Teflon or whatever in it to reduce friction where the strings enter the slots. If you have both, you're golden. Or if you have a tremolo system with a locking nut, then it doesn't really matter since there's no movement on the bit of the string between the nut and the tuning machines.