Hi...thanks for sharing your story. This is a perfect example of the chain of events that occur often before an accident. And we all know that we have been at some point of that chain before and it's about being able to recognize and breaking it. It's really important that we share these things around.
To answer your questions...
Pilot reports are critical, and this is why. Had you been in a more comfortable position, this would have been great opportunity to share with other pilots contemplating the same thing you were just an hour ago.
Visibility is visibility regardless of haze/fog/clouds/smoke. Because weather is always changing, the forecast/report are only for your reference and it's up to you to determine what it is during your flight, and that is what you are responsible for. So...good question, how does one determine visibility in the air? Something to think about in your local area. Is there a reference point ... mountain/hilltop/tower that you can look at as you depart? (Sugarloaf Mountain is how far from your airport?) Chances are if you are questioning it, it is below your minimums. So...if your minimums are 7 SM, probably you were in violation. An interesting point from Instrument Flight Rules, when you are landing on an approach, the reported visibility is also a guideline. When you actually break out and are landing, it is up to you to confirm that you have the visibility required to land. ie, you should know your lighting systems/runways markings so you can confirm vis and know that you are legal.
Tony is absolutely right here, GPS is not going to help you here. Making sound decisions so that you aren't relying on GPS will. Instrument Rating will.
I, too, am unfamiliar with ADIZ, but essentially, ATC is there to help facilitate your flight. If you are getting into conditions that are not to your liking, and possibly unsafe, and not legal...then absolutely, tell them you need to turn around. Tell them the situation. As Tony said, they are people too. Do not let the intimidation of talking to ATC deter you from making the safest decision.
It sounds like you learned a lot from this, and my only other thought is to be aware of the process that you experienced here and try to recognize it a little sooner. As soon as the visibility decreased, make the decision to go home. I know landing at another airport and not being able to return is an inconvenience, but certainly one that would seem ridiculously inconsequential if something more serious had occured. And so taking off again, knowing the conditions were poor, the light was getting low...maybe not a good idea. As you can see, a lot of little things started to add up...leading to no pre-landing checklist.
Thank you so much for sharing this with us all, and I hope that we take something. I have a couple of stories myself...which of course will share in due time
Take care and fly safe.