1. One ‘non-Calvinist’ approach is to highlight the ambiguity within the passage itself, as BruceReichenbach explains (italics his, bolded emphasis mine):
“Does the passage teach that God does or works everything in conformity with his purposes, or does it teach that everything God does he does in conformity with his purposes? The grammar of the sentence does not force us to adopt one interpretation over the other. For example, one can say, “John does everything very slowly.” From this we would not infer that John does everything, only that everything he does he does slowly.” (‘Response to Feinberg’ in Predestination & Free Will, Bruce Reichenbach, eds. Basinger & Basinger, p.52–3)
Paul, according to this view, is not saying that God decrees all things but all that He does decree or act upon He does so in conformity towards His will. This both avoids the complications of an all-inclusive divine decree and affirms the goodness, justice, power and wisdom of God in all His work.
Alternatively, God could be said to be working with and within all situations to ‘realign’ them more towards His ultimate aims. The idea of a plan also makes better sense this way — when there is at least some element of uncertainty, flux, opposition, ‘undesirables’, etc. — rather than in the case where every minute detail has been pre-set ahead of that being planned for. Surely it requires more power and wisdom to ensure that one’s ultimate goals are achieved in spite of resistance, than to dictate everything from the beginning. The former would represent a real victory; the latter wouldn’t even be a real battle.
2. On the other hand — assuming Eph1:11 is teaching that ‘God does everything’ — instead of interpreting ‘everything’ in an absolute way, we could acknowledge the contextual limitations imposed on the verse. ‘Panta’ (‘everything’, ‘all things’) ought to be understood in light of the focus or theme of the passage and not uncritically used in an all-inclusive total sense. This is obviously seen in the following passages:
John 19:28, “Later, knowing that all was now completed, and so that the Scripture would be fulfilled, Jesus said, ‘I am thirsty.’” (focusing on Christ’s atoning work)
Acts 17:25, “And God is not served by human hands, as if he needed anything, because he himself gives all men life and breath and everything else.”(focusing on ‘existential’ provision and/or basic sustenance)
Rom 8:32, “He who did not spare his own Son, but gave him up for us all — how will he not also, along with him, graciously give us all things?” (focusing on ‘all that we need in Christ’, *smile*)
1Cor 6:12, “’Everything is permissible for me’ — but not everything is beneficial. ‘Everything is permissible for me’ — but I will not be mastered by anything.” (focusing on food)
1Cor 12:6, “There are different kinds of working, but the same God works all of them in all men.” (focusing on spiritual gifts)
In the above, the authors of the passages implicitly limit panta to whatever topic they were discussing; the word simply wasn’t meant to be taken in an unqualified way. And this could be the situation we face with Eph 1:11. What is the focus in this case? Jack Cottrell offers a suggestion (emphasis mine):
“This focus (of Eph 1:11) is ‘the mystery of his will’ (1:9), which is the uniting of Jews and Gentiles together into one body, the church (3:6). To say that God works all things after the counsel of his will means that he does whatever is necessary to accomplish this purpose i.e. the gathering together of Jews and Gentiles under one head, Jesus Christ.” (‘The Nature of Divine Sovereignity’, Grace of God & Will of Man, ed. Clark Pinnock, p.116)
Although this explanation is less solid than I would hope, it can also be pointed out — as Cottrell did (ibid. p.116, n.83) — that Calvinists also tend to limit the scope of ‘panta’ when the passage in question impacts their doctrine negatively, the most prominent examples being John 12:32, 1Tim 2:4, 2Pet 3:9 i.e. the famous ‘universal atonement’ proof-texts. (It’s interesting to see how Arminians detect in Scripture God’s love for all, whereas Calvinists read only the universality of God’s control. Naturally, I prefer to use the former ‘grid’ for interpreting Scripture, not to mention Eph 1:11)
Finally, to complement Cottrell’s view (and combine it with the first ‘Arminian-inclined’ approach to addressing the verse), we could paraphrase the key section in 1:11 to read, “…having been predestined according to the plan of Him who acts in everything in order to bring conformity to His plan of uniting Jews and Gentiles under Christ…”. God is even now implementing His project — which no doubt ‘hits’ everything in creation — to ensure that soon there will be ‘no Greek or Jew, but Christ in all.’