Ehhhhh.... as a player who almost always plays ADC and plays Varus many games, I'm not so sure about this one. It seems to be a good direction, but as others have said, it takes away a lot of his interesting gameplay and homogenizes him quite a bit.
Here's what I like:
These two points are the most general, but I can see from the post that OP is thinking in the right direction. But...
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I don't like the idea of Blight being his passive. The On-Hit is a big part of lane for me and putting points in it later feels very powerful.
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I don't like having Piercing Arrow split for it's "bonus effect". This is because I think it would feel cartoony and slapstick/gimmicky. Perhaps, instead of splitting, it gains size(width), has no damage falloff, and more range/inertia when proccing 3 Blight Stacks?
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His new ult is really boring. It would feel really badass to hit that "R" key and shoot super fast, but that isn't really Varus's gameplay. I would rather see a mechanic where Varus gains attack speed for proccing 3 Stack Blight as part of Blighted Quiver.
These qualms mean that this kit, if implemented to live, would make me come to these forums and whine about how they ruined Varus for me. Here is a version of this rework that I would like better.
Passive: Hail of Arrows - When Varus slays a unit, detonates 3 stacks of Blight, or attacks a target affected by his ultimate, he fires an extra set of arrows around the area, dealing minor AD scaling damage to champions (which procs Blight, and does not affect minions) and slowing all enemy units who walk through the area.
Q: Piercing Arrow - Fires an arrow with similar range, damage, and scaling to live, and if Piercing Arrow procs 3 stacks of Blight, the arrow ceases to have per-target damage falloff, becomes slightly wider and cooler-looking, and gains speed, continuing in a line from the target as long as the original charge range of the arrow.
W: Blighted Quiver - On-Hit magic damage removed, possibly lowered % max health damage. Targets which are hit by 3 stacks of Blight now take bonus effects.
E: NEW Burning Vengeance - Varus's next attack gains 25/35/45/55/65 range, deals .2 total AD extra magic damage, and can proc Blight. In addition, if this ability procs Blight, it adds one additional stack of Blight. Starts with a fairly high cooldown (8/9 seconds) and scales with level down to a very low (2/3 second) cooldown. 50 or so non-scaling mana cost.
R: Tendril of Corruption - Similar damage and scaling to live, but with these effects. If this ability strikes a target with 3 stacks of Blight, it shreds their armor and magic resist over time by (1%/2%/3% per second) until the ultimate is no longer in effect. In addition, Varus attacking the affected target of his ultimate makes his "tendrils" move faster toward their new targets. Possibly lowered damage/raised cooldown.
This kit feels more like the "Vengeance Archer" I would feel good and powerful playing, and I hope I have left sufficient openings for balance in the kit. If you feel it is too strong, good options to remove are the loss of falloff damage on "super arrow", champion damage on passive(Still procs Blight), or DOT shred on Tendril of Corruption.
TL;DR: Varus E goes on to his passive and goes off when he does good "Varus things", E replaced with an AA reset that procs Blight, instead of splitting, Q goes faster and hits harder after hitting a "Blight Target", and W lost the On-Hit damage(basically moved to E). Proccing Blight at three stacks incurs bonuses on all his abilities.