On your point about what our economy might have been outside the EU, it's probably a bit of a distraction to try and argue the counterfactual as it's pure speculation.
On our membership of the EU giving us more 'clout' against the US and China, it may well be the case that the EU together has more clout against China than the UK would have on its own. But that is not the same thing as saying the EU's clout, with the UK as a member, means the UK has more clout. It doesn't - a club to which it belongs has that clout. The club itself may choose to use its clout to do things that are not in the UK's interests at all. Indeed there are numerous documented instances of exactly this happening.
It's also worth pointing out that talking of the EU as if it were the 'top table' is in many cases false. Much of the regulation the EU issues as directives emerges from international bodies such as the IMO and Codex Alimentarius. These bodies are formed of national representatives and industry experts, and produces standards that apply worldwide in the interests of making commerce run smoothly. (Apologies if you know all this.) Representatives of nation states are able, on these bodies, to push for the interests of their nations. Increasingly, the EU seeks to supersede its member states' individual representatives on these bodies, meaning that at these crucial 'top tables' where key international standards are agreed, it replaces member states' multiple representatives, each able to advocate for his or her national interests, with a single EU representative who then has to be lobbied elsewhere for the national interests of member states. In this sense, EU representation gives us not more influence but 1/28th of the influence we'd have if we represented ourselves.
More profoundly though, I think increasing EU integration is the wrong response to globalisation. It may give the EU as a whole a superficially larger size, but internally it is too fragmented to act with any coherence, as we have seen in the refugee crisis. And there is no meaningful democratic engagement at European level, meaning that as a democracy it is not and could never be legitimate. Put simply, the peoples of Europe don't want a United States of Europe. If the question was put to all 500m EU citizens as to whether they wanted to form a federal superstate, do you really think the answer would be 'Yes'?
Given that, and the structural weakness of democratic accountability within the EU, while it might be superficially true that its larger economic size makes it a more formidable player against China and the US, its lack of real democratic support and accountability means that this greater 'clout' is likely to be wielded not in the interests of ordinary electorates but in the interests of the elites and big business.
Globalisation is happening, whether we like it or not. I think if we are to meet it in a way that takes the interests of the little people into account, that means not weakening nation states by subsuming them to a supranational federation but strengthening them and ensuring accoutability at a level where people can feel genuinely engaged. Otherwise we will end up with TTIP after TTIP, in which the negotiators say - like Cecilia Malmström - 'I don't take my mandate from the European people'.
That, at the heart of it, is why I think the EU is the wrong answer to a very real question.