I am always glad to jump in on a discussion for Garen as he is my favorite champion.
(First off, thanks for pointing out the obvious counterclaim that he can't be linearly buffed right off the bat, it prevents the argument from getting used later ona and allows the discussion to go straight to the main point.)
Before I get onto the topic of your proposed changes there is something we need to get out of the way first and foremost. What makes Garen who he is? What are the fundamental strengths that themes the pull him together into the manly beyblade we all and love? Three things comes to mind. Silence, Damage mitigation and killing power, because that is in essence all he really has going for him.
Now what are his weaknesses that prevent him from being used competitively? Lack of crowd control, reliance of flash for engages and inability to scale into the late game.
Now on the the meat of the topic turning his Q into a leap is something that we have discussed quite often on the forums actually; this is because it solves one of his essential problems that preent him from being use and that is his over reliance of flash. Most Bruisers or tanks have a solid method of quickly engaging into a fight and being near the enemy that doesn't involve running straight at them. Maphite has his ult, amumu has bandage toss, Vi Q/R and Darius' pull are all examples of this. Garen flat out does not have that ability, all of his engagement power relies completely on running straight at the enemy, and this prevents him from being able to reposition and get to the fights he needs to be in. Adding passive movement speed gain to it is a new one though and certainly helps detract from the issue that not having an on demand slow cleanse brings.
On another note I would like to add that no matter which way you look at it, taking away or adding power to Garen in any way is tricky. Decisive strike already does a TON of damage, especially if it crits. Your suggestion would make that power even more ridiculous than it already is by halving the cooldown and having it apply an AoE. However it might balance out with the removal of his silence which is a different issue altogether I will get on to below.
On the topic of removing his silence I honestly don't know what to say to this one. His silence, being single target and also his only engagement and his only form of crowd control is by far one of the most essential parts of his kit that allows him to focus down enemy squishies. As it is his ONLY form of crowd control removing it in favor of a slow is a HUGE downgrade to a champion who already lacks hard crowd control. This would only further remove his ability to tank and peel for his team, and aside from doing damage that is his job as a bruiser. Honestly the only real suggestion I can think of for this was what I discussed earlier, add a leap to the Q but leave it otherwise unchanged. The thing is he HAS t have some form of crowd control as a bruiser otherwise his would be worthless, and a slow is by far the weakest form of crowd control in the game (except for wither but that is a MASSIVE slow)
So what other thing should we be looking at right now that is essential for his role? When it comes to damage mitigation Garen has it down pat. Courage is an extremely powerful ability, basically a smaller version of Alistairs ultimate and as such allows him to mitigate damage just fine and with the passive element and perseverance taken into account Garen is naturally tanky. Any buffs to Courage would outright break it.
When it comes to his spin there is really not much we can do. It is an absolutely essential part of Garens kit and no one would want it removed or changed in function. The only things I can really think of are to
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Remove the slow from going through units, Garen is already forced to use his Q all the time anyway, why should he slow himself?
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Remove the damage reduction to Minions, I honestly have no idea why this is here in the first place.
Now we should address the elephant in the room on Garen's kit. His ultimate. Judgement is a cool ability to be sure, but it honestly....sucks. In comparison to other executes it is not spammable, does less damage or has too long of a cooldown with no incentives to make it into a unique and powerful ability. To give an example here are some other common execute based ultimates.
Same cooldown, Does True Damage, has an AD ratio, has a reset mechanic to allow multiple dunks.
Literally just a better version of Garen's Ultimate, it does 5% less missing health and for that trade it is also has an ad ratio, global range. lower cooldown and is an aoe
Ranged Aoe, lower cooldown empowers her ad and abilities
So in comparison to that Garens bread and butter execute is a bit...lacking. My possible suggestions are follows.
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Make it into an aoe. Primary Target takes full damage while enemies caught in the blast take 50% of the base damage (no execute) and are knocked back. This would make it unique and address the issues of Garen not having crowd control.
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Make the skill true damage and change nothing else, this would make the skill powerful and feel worth being a single target, long cooldown ultimate with no crowd control. It would basically be a true death sentence to low health targets and allow it to do the job it was meant to do properly.
