400/500 hp healing on 4 seconds
Wow, what items are you buying? I've had a lot of trouble finding out how to build 1,500 to 2,000 AP on Sona. No matter what I build, I just can't ever figure out how to do it, particularly when I'm also maxing out CDR. What's your secret?
nor the movement speed
I actually disagree with you. Personally, I think that having a 100% uptime on a speed boost with only one point is stupid, and I don't think it has any place on her kit. I would toss this in an instant. It's power she definitely doesn't need.
Actually, I kind of disagree with everything you listed. You're complaining that Sona's heal doesn't have counterplay, but honestly, neither does her Q or her E, and her auras have such a huge range that I'm barely even willing to classify them as counterplay. All of her basic abilities lack counterplay in some major way.
As for your proposals, I dislike two of them because as the game goes on, I'm never going to be able to actually play around those. I also think you vastly underestimate the amount of power available in the shield compared to the amount of power in the heal.
heal on ally is now based on how close she is to her allies,
The ally who is weakest changes way, way too often in a teamfight for it to be realistic for me to constantly be near the one who is most hurt. The only way this would work is if it was worth saving the heal to try and get closer to a teammate who was hurt more, but that's always a bad idea because your number 1 priority with Sona's W is getting the shield off. The shield is much stronger than the heal, and I'm never going to make a decision to make the heal slightly more effective if it compromises the W's effectiveness at all. It would be a terrible decision, so it's a decision I don't get to play around.
I see no value to this proposal over straight numbers nerfs. The decision it introduces is so heavily overshadowed by the more important function of the shield that it will never be an actual decision in any fight outside of the laning phase. False choices are annoying, and should be avoided.
-make her healing the nearest ally instead of the most wounded ally.
Again, I actually have very limited decision making power around this ability. Maximizing the shield output will almost always be more important. On top of that, it's just needlessly annoying. This creates much more frustration for the Sona player than necessary because their heal will not be doing anything effective in most teamfight situations, and it will not be worth playing up far enough to make the heal work when it both puts you at risk and decreases your ability to preform the much more important task of providing auras. If we wanted to reduce the heal's effectiveness, we could just nerf it, and that wouldn't introduce the frustration of a false choice.
-make her heal projectile disappears if it hits an enemy,
This one is a more interesting proposal. It actually introduces a source of proactive counterplay instead of just imposing a false choice on Sona, which I like. It's always better if you place the means to counter a champion in the enemy's hands whenever possible. The biggest issue I see with it is that Sona's projectile speed is very fast, which makes the counterplay to just stand between Sona and whoever you think will be hurt the most a second or two from now. It also means that the reward doesn't feel good for the enemy. A small green projectile quickly shoots into my champion instead of theirs. That really lacks viscerality.
To be honest, I don't think Sona's heal is a problem, because it's really just the same as the rest of her kit. Her Q is autotargeted, her auras are huge and extremely easy to tag people with, and her power cords only require an autoattack to make use of. Everything she has is either low counterplay or direct stats. Some people will be annoyed more by her near-guaranteed damage, some will be annoyed by healing, and some will be annoyed by the auras being essentially free to apply (you can see all of these complaints on the boards right now), but the final issue is that everything she does lacks counterplay. She needs more of it across her whole kit.
Personally, I think that the E and the aura ranges are the smartest places to start. Making them less forgiving would increase the risks Sona would have to take to do her job while actually forcing her to take those risks. With your proposals, I could justify getting an ineffective heal if doing so let me use the auras better. There will be no way to justify not getting close enough to allies to use a shorter ranged aura.