This is one of the most controversial areas of running.
Shoes:- pronation; gait analysis; foot strike; orthotics; biomechanics etc.
As you say, opinion is divided. It will always be that way. You will get some people that will swear by one way and others another.
I think that you need to find an approach that works for you and that you are comfortable with and stick with it. I don't believe there will ever be a consensus or one size fits all approach.
I have no expertise in this area but for me, I would consider addressing the imbalance through exercise. There are exercises targeted at over pronation - which in itself isn't a fault, it's just what some people do naturally so does it need correcting? I think a lot of this is marketing targeted at our own insecurities.
If you go to a shop that sells minimalist or barefoot shoes they will tell you that's best and will promote that, if you go to a shop that uses gait analysis then they will try to sell you shoes based on that approach.
If you are doing stretching exercises then it is recommended that you warm the muscles up first as stretching cold muscles can cause injury.
If tight muscles from running are a problem for you then there are a few things that you can do to help. Go swimming, do swimming drills, (you can find a whole host on youtube), do dynamic stretching exercises mid run, do some flexibility exercises mid run or after your run. Deal with any inflamation with for example, ice bath straight after a run, warm bath in the evening, foam roller, massage or the stick.
As I said, find one approach you like and stick with it, you don't have to have big clumpy shoes if you prefer barefoot, jut be aware of the pros and cons and work with what you have.