Assuming that the Ezreal isn't sloppy enough to be hit by grenades (although you should always try when appropriate), it would be best to position your turret in the way of your minion line for a buffer tank. Do remember that his Mystic Shot also costs mana, and with clarity and teleport, you should be able to overwhelm him. If, however, you're in a position in which you have no turrets, make sure to just take a step back in your siege to set up some turrets in more conservative positions so you could continue forward with significant destruction of enemy minions.

You play Heimer-Slinger as I do. I salute your blonde-fro!

I can personally vouch for this guide's viability. I laned mid vs. mid as heimer against heimer, and my opponent used this guide to the letter (Could it have been you, Thth? I'm SomethingGiant in-game, this game was played in the last few days). Best heimer I've ever laned against. Despite this, I destroyed his tower by 10 minutes in without my tower taking a single hit of damage, and my team won the game easily. I went 11-1-6, opponent went 1-6-X.

With this success in mind, and my personal experience, I'll venture to suggest a few changes to your guide.

Summoner Spells: Teleport/Clarity is the only option. Never consider anything else. Use Clarity whenever it's up, whenever you have used enough mana so that none of Clarity is wasted.

Runes: AP quints, AP blues, AP per level yellows, magic pen reds. This gives me 24 AP to start, an additional 17 AP at level 18, and a little under 10 magic pen.

First Item: Doran's Ring (+hp pot). AP, mana regen, HP. The AP and HP last until mid-game, and the regen is essential for early game spam.

Rushing to mid may be viable, but I have never done it before. It is more important to get the 6-second faster firing rate on your first turret, and push as hard as possible as soon as possible.

Take turrets and grenades until level 8, every game. At level 8, grab your ult, and at level 9, grab turrets again. Then Ult > Grenades > Rockets.

Don't worry about damaging the opponent's tower until level 4. Don't use your grenade until level 4 except for self defense. AT level 4, spam your grenade to hit your opponent's tower whenever it's possible and safe.

Whenever you have a creep wave of 5 or more at their tower, drop a turret and back off; this turret will do lots of damage very quickly. Be sure to back away from the tower whenever you do this, as you will often draw tower fire unintentionally.

Keeping your turrets alive is mostly about proper placement. Think about who you're against and what abilities they have. Wide placement against AoEs, within your minion line against skill-shots, clumped against ashe's volley, keep one just out of range of their minions when against someone who tries to harass. Play it by ear, and find the placement that keeps them and you alive most effectively, while dealing as much damage as possible to enemy minions. Toss grenades preemptively to ward off auto-attackers, auto-attack THEM, and keep your turrets further back if it becomes a problem.

At 1330 gold, blue pill and buy Tear and boots. Port back in onto one of your turrets if it's being attacked (As it likely will be in your absence). At this point, push as hard as possible, until their turret is destroyed. Their turret should go down between 7-12 minutes in.

When their turret is down, plant up to max turrets in a defensive formation, then go and grab golem. This should be at about level 9. After golem, push both side lanes. 3v2 this will be laughably easy with the golem buff. 3v3 it will be simple, but will require a little more patience. At 1985g blue pill and get Mejai's and sorc boots.

Refer to the Oppenheimer guide unless it directly conflicts with this one. Thth really does know what he's talking about.

Item build after Mejai's, Boots, and Tear:

Zhonya's
Tear -> Archangel's
Rylai's
Zhonya's
Get red and blue elixirs after this, and stop going out of your way to farm minions. Your allies need them more.

SomethingGiant: Your opponent was certainly not me, as I have never lost to another Heimer Your guide certainly does not deviate much from mine, and your victory was most likely attributed to your skill rather than said deviations.

As for the rest of your guide, it's certainly viable with the differences being ones that excel and falter situationally. Two counter-points though:

You still get the attack speed boost from rushing the turret, since you'll have your mana regenerated back up and the cooldown finished by the time the minions get to mid.

Secondly, your build lacks a void staff. The magic penetration is quite essential in boosting your damage, especially to towers. (Although I see that might be a mistake, due to your build having two zhonya's)

Thth, we should have a practice game.I have also never lost against another heimer in memory, and I've had about a 2:1 win ratio since the patch (with ~15 straight wins at the moment). I'm really interested in seeing how you play him.

If you're building another turret immediately, why bother in the first place? With no clear advantage, and potentially letting your mid opponent learn who he's against very early on, it may actually have a bit of an overall disadvantage.

Void Staff is a good item, but unless my opponents are stacking lots of MR, i wouldn't take it over another Zhonya'. I haven't done the math, do you know at which point it becomes viable to buy void staff over Zhonya's, with sorc boots?

Cyst: Could you explain how my guide is "bad"?

You only differ in getting tear first rather than going for chalice, as well as RoA. While it's certainly viable, you've not explained how my build is not.