I understand how it can be frustrating combating Poppy on the battlefield, whether it be in the top lane or the jungle. Personally, I main Poppy as a support champion, what with her amazing utility-based kit. Though you do make valid points in your post, stating the problem with the hitbox range of her E. I may speak from experience that there have been multiple instances that I had landed a successful E (Heroic Charge) when the champion was not fully in the range of the skill. Other than that, I personally fail to see many flaws with her new kit.
Damage-wise, I understand that it doesn't take much more than one or two damage items to make her the heavy-hitting bruiser we know and love her as. But in that aspect, I can definitely list a few champions who could more immediately use some damage nerfing. And as far as her ult goes, I find the damage is deals to be rather miniscule. In all honesty, I hadn't even noticed it did damage at all until several days after her rework, having taken a dragon kill from the enemy team with this method when I attempted to knock them away from it. All in all, as far as damage goes, I find her ult to function as an execute an enemy champion who's juuust close enough to land the pre-windup smack of the skill.
Thankfully, I also have tips that could hopefully help you against Poppy. The most crucial part of fighting and countering her, is your positioning. Poppy relies heavily on where her enemies are positioned, determining who she can and can't lock down with her E in order for her team to engage on them. If Poppy is pursuing you, try to maintain in the center-most area of the lane, as well as having minions in her way to slow down the chase. If she had already used her E, then your window of opportunity for a counterattack opens for your team to focus the yordle down and take her out.
Another note that could help, is to remember that 9/10 Poppy players will use her in either the top lane or the jungle. In those instances, the players will most likely be prone to building her with AD and Health stats. While this is effective in many cases, this still leaves the yordle vulnerable. Having little focus on her resistances, players could make potentially quick work of her if teamed properly. She may be strong, but Poppy is a long shot from un-killable.
For the 1/10 players that use her as a support champion (namely, myself), it is fairly easy to keep Poppy under lock-down with a mage-type support (ex. Sona, Soraka, Nami, etc..) that has the range to constantly harass her and the AD carry. Poppy's only attack with mild range (besides her ult) would be her passive (Iron Ambassador), which throws her buckler to deal damage and grant her a shield if picked up. The player would also feel pressured to purchase a magic-resist type item, leaving her armor unattended for the enemy AD carry to deal harassing damage.
All in all, I find Poppy to be a fairly balanced champion as opposed to others (Cough cough Fiora..). Her utility-based kit makes her a great addition to any team, but not quite overpowered enough to be an immediate threat on Summoner's Rift. I hope this helps spread a light on a subject many have contemplated before, and that it will assist you in your future matches. Best of luck! 