Jax's kit synergy

Hello, I'm a master tier top laner who's most played champ in ranked is . He's been my favorite character since season 1 and I still continue to play him even though I know he's a little outdated. Although I feel he is outdated, I think he isn't too far from being "balanced". Nowadays, his win rate usually sits around 49~ percent, which I'm not saying completely decides if he's balanced, but it is a good indication. Although I think he's decent, there isn't a single meta top laner that I would pick Jax in if someone told me to pick the best champion for the job. What Jax excelled at is now outclassed by other champs. You want a split pushing ad top? Fiora can duel almost anyone and doesn't take three items to become a threat. Are you versing a melee fighter? Well Jax's dodge is good against melees, but malphite provides much better team fight, is much easier to play, oh and also doesn't take forever to scale.

My ideas: I don't think Jax needs massive base stats to be good like he used to, but his kit is clearly outdated and should receive something!

Here are some ideas I have. They're all speculation of things I've thought of

-Auto range: 125? He's using a lampost not a butter knife. Why is his attack range so low??

-Q, Leap strike: Has a flat mana cost of 65? Shouldn't the mana cost start at like 40 and go up each time you level it? Also, maybe make auto reduce its cd by 1? Whenever I use Q, I always save it until I need to gap close. In a 1v1 fight, you are punished for using leap strike early as its your only way to gap close and guarantee you land your E. Another idea might be make it reduced every time you hit something with empower? Of course this might need some cdr adjusting to make it balanced, fioras jump is 16 at level 1, but can be reduced very easily.

-W, Empower: Mundos E now increases his next attack AND it's attack range, why not empower? Another idea might be to make it so when you use empower your auto cant be cancelled when stunned. The most frustrating thing when versing riven or renekton is when they stun you and dash away leaving you with no way to trade. You have a mana bar, they dont. Sure you can use all your abilities and trade back, except that means using your jump, and your dodge, better hope you dont get ganked ;) cause your level 1 e cd is 16 seconds.

-E, Counter Strike: Jax's bread and butter and what makes Jax who he is..except if your basic attack is an auto enhancer you only dodge the auto attack portion of it, such as Nasus' Q. So can dodge everything for .75 seconds, even karthus ult, but Jax cant dodge all auto attacks and auto attack enhanced abilites? It's very inconsistent on what it can and can't dodge. The only way to know is by testing it yourself or looking it up on wiki This could also be another move where its Cd is reduced by autos, although it would still probably be more useful on his q.

-R, Grandmasters Might: Honestly, not really much to say about this move. For the most part it's probably fine where it's at. One complaint I have is sometimes I die before being able to cast it, or get put really low. It doesnt matter how much armor and mr I get when my Hp is already around a quarter. Maybe make it able to cast while stunned? or make the duration longer so you can preemptively use it?

Although I am unsure how the new preseason changes will affect Jax, I believe his outdated kit will still remain leaving the only Jax players to be some old Jax enthusiasts such as myself. Jax has lost his identity, and needs help getting it back.