There is no way to become a major player in the EU - it's simply impossible. The UK routinely loses virtually all the voting positions it takes in the EU Parliament, so basically, it faces a choice between keeping its current positions and having no influence, or adopting the same positions as most of the other countries and by definition not having any influence.
To think that the UK, which is relatively right wing, can change the basic direction most of the other countries are travelling (relatively left wing), seems to be naive. There are only two futures for the UK - in, and forced to constantly do things against its will until it eventually ends up with an EU government that doesn't represent what the populace thinks (nor care), and out, probably triggering a trade war with the countries whose politicians treat the EU as a religion and therefore must punish heretics.
As you say, the EU would be much more effective if it was more federal.
If you define "effectiveness" as "successfully harmonising laws and regulations" then yes, of course it would, sort of like if you define an "effective government" as one that enforces the rule of law eliminating the rules of evidence would make it more effective.
Most people have wider definitions of effectiveness though, for instance, creating prosperity and protecting various liberties. Measured along these lines, it's not at all clear that the EU would be more effective if it became larger and more powerful. The EU so far as a very mixed track record of creating prosperity, with the Greek fiasco being the number one case of where things went wrong but it's far from the only example. It is instinctively protectionist and has massive problems with the French, in particular, vetoing things that'd make sense for literally everyone but which would upset some French minority ... for instance the protection of the desperately dull French film industry constantly causes issues, the reason the EU Parliament switches between two different places at massive cost and waste is because the French would veto any attempt to stop it, and so on.
I'm undecided which way I'll vote myself, but let's not pretend that the UK is holding the EU back from greatness. It's trying to hold it back from federalism (and mostly failing), but that's not the same thing at all.