Does Galatians post-date 1 Corinthians?

I've been doing some thinking about Pauline Chronology recently and one thing that consistently surprises me is that 1 Corinthians is so often held to post-date Galatians. I don't think this is right. I think it more likely that Galatians was written after 1 Corinthians, but before 2 Corinthians. The strongest evidence for this is the role played by the collection in the Corinthian letters and the epistle to the Romans:

1 Cor. 16.1-4: ‘Now concerning the contribution for the saints: as I directed the churches of Galatia, so you also are to do. On the first day of every week, each of you is to put something aside and store it up, as he may prosper, so that contributions need not be made when I come. And when I arrive, I will send those whom you accredit by letter to carry your gift to Jerusalem. If it seems advisable that I should go also, they will accompany me.’

2 Cor. 9.1-4: ‘Now it is superfluous for me to write to you about the offering for the saints, for I know your readiness, of which I boast about you to the people of Macedonia, saying that Achaia has been ready since last year; and your zeal has stirred up most of them. But I am sending the brethren so that our boasting about you may not prove vain in this case, so that you may be ready, as I said you would be; lest if some Macedonians come with me and find that you are not ready, we be humiliated - to say nothing of you - for being so confident.’

Rom. 15: 24 For I do hope to see you on my journey and to be sent on by you, once I have enjoyed your company for a little while. 25 At present, however, I am going to Jerusalem in a ministry to the saints; 26 for Macedonia and Achaia have been pleased to share their resources with the poor among the saints at Jerusalem. 27 They were pleased to do this, and indeed they owe it to them; for if the Gentiles have come to share in their spiritual blessings, they ought also to be of service to them in material things. 28 So, when I have completed this, and have delivered to them what has been collected, I will set out by way of you to Spain.

It cannot escape the most cursory of readers that Galatia has dropped out in between the writing of 1 Corinthians and 2 Corinthians. Paul is still on good terms with the Galatians in 1 Corinthians, and has recently given them directions concerning the collection. By 2 Corinthians and Romans, they are no longer mentioned as participants in the collection. The rupture with the Galatian churches, to which the epistle to the Galatians bears witness, has occurred in between the writing of 1 Corinthians and 2 Corinthians. Paul has lost those churches, and Galatians is his last desperate attempt to win back people he sees as apostate.

That 1 Corinthians was written before the Galatian crisis is clear not just from the role played by the collection but also by comparing remarks made in the respective epistles. Consider the following, one of the most remarkable things Paul ever said:

1 Cor. 7.19, Circumcision is nothing and uncircumcision is nothing. Keeping God's commands is what counts.

The very problem he faced in Galatia was that his opponents were stressing circumcision as a commandment of God. He would not have said something like that after the difficulties at Galatia. Indeed, the Galatian experience encourages him to reformulate the above remark:

Gal. 5.6: For in Christ Jesus neither circumcision nor uncircumcision has any value. The only thing that counts is faith expressing itself through love.

Gal. 6.15: Neither circumcision nor uncircumcision means anything; what counts is a new creation.

The similarity in tone between 2 Cor. 10-13 and Galatians has often been remarked upon, and it is a similarity that makes still more sense if 2 Corinthians and Galatians were written close in time to one another.