Sovereignty is relative. We are sovereign to a degree, and we are independent to a degree. The UK has signed a multitude of international agreements which in one way or another limit this sovereignty and our independence. Largely we enter these positions freely because we realise that we all benefit being subject to WTO regulation, and we all benefit from being members of the ECHR. In signing up to these we pool sovereignty. Yet this sovereign ability to act is also material. In the Suez Crisis we used our sovereign right as a state to attempt to enact regime change in Egypt. The US slapped us down. We weren't as sovereign as we thought we were. We did the same to Argentina in the Falklands.
The point is this idea of sovereignty is subject to exogenous forces that we cannot completely control. We are subject to this political gravity whether we refuse to see it or not. The same is true of the EU. We would not suddenly become markedly more sovereign after a Brexit renegotiation - we would sign new treaties which limit this sovereignty; we would have to abide free movement, a membership fee and EU law and regulation as a price to do business with the world's single largest economy and our biggest trading partner. We would not float above all these forces. At the same time our sovereignty is furthered reduced because we do not have a voice on these laws and regulations which will still apply to us. We just have to swallow them like Norway does.
That is not sovereignty - that is practically less control over our own economy than we presently enjoy! It is more democratic if we have an EU commissioner and MEPs fighting our corner and representing us in Brussels, rather than tapping on the windows from the outside. Inside the EU we can hold it to account, outside we can stamp our feet and go red with impotent rage. It doesn't matter we'll be subject to the economic gravity of the EU. Cameron is exactly right when he talks about the illusion of sovereignty if we leave.
I agree with what a lot of what you have said however, we don't need to abide to free movement and a membership fee just to do business with the EU. We can have trade agreements outside of that, just as other countries do. For example, US trade with the EU, as do China and Japan and a host of others but they don't have to abide by EU free movement rules or pay a fee for the privilege. However if we want closer links than most, similar to Norway and Switzerland then yes, we do abide by the free movement rules and pay a fee without having a say about those rules.