Q:

Exegesis of Galatians 4:12. Is the presented analysis valid?

Galatians 4:12 New American Standard Bible (NASB)
12 I beg of you, brethren, become as I am, for I also have become as
  you are. You have done me no wrong;
Galatians 4:12 King James Version (KJV)
12 Brethren, I beseech you, be as I am; for I am as ye are: ye have
  not injured me at all.
Galatians 4:12 English Standard Version (ESV)
12 Brothers,[a] I entreat you, become as I am, for I also have become as you are. You did me no wrong.

Analyzing Paul's faith in progression
Ethnic & outwardly observant religious Jew emphasizing that obeying Jewish Laws and rituals is important
-----to------->
follower of Jesus Christ (but not a Judaizer (i.e. Jews who acknowledged Jesus Christ, but also emphasizing that obeying Jewish Laws and rituals is important))
Analyzing Galatians's faith in progression
Most likely majority Gentiles who obviously did not emphasize that obeying Jewish Laws and rituals is important (I am assuming there were no Jews among the Galatians)
-----to------->
follower of Jesus Christ but manipulated by Judaizers (i.e. Jews who acknowledged Jesus Christ, but also emphasizing that obeying Jewish Laws and rituals is important) to follow said Jewish Laws and rituals

Keeping the aforementioned analysis in mind, this is how I view (Galatians 4:12)

I beg of you, brethren, become as I am

Paul is urging the Galatians to be a follower of Jesus Christ (and
not emphasize that obeying Jewish Laws and rituals as being important)

for I also have become as you are

Paul is stating that he himself, by currently not being captive to Jewish Law and rituals became like the Gentiles since Gentiles obviously do not emphasize that obeying Jewish Laws and rituals is important
Is there something incorrect and/or missing from this view?

A:

The context of Galatians 4 suggests that, yes, Paul was inviting the Galatians to abandon the Mosaic Law with its precepts and ceremonies when he said "become as I am." Here is the context. Notice that only two verses earlier, Paul rebukes them for observing Mosaic "days, and months, and times, and years."

Galatians 4:10-4:12 (DRB) You observe days, and months, and times, and years. I am afraid of you, lest perhaps I have laboured in vain among you. Be ye as I, because I also am as you: bretheren, I beseech you: you have not injured me at all.

This is also how St. John Chyrsostom understood Galatians 4:12. You will notice, however, that Chrysostom seems to think that there actually were some Jews among the Galatians.

"I beseech you, brethren, be as I am; for I am as you are." 
  This is addressed to his Jewish disciples, and he brings his own example forward, to induce them thereby to abandon their old customs. Though you had none other for a pattern, he says, to look at me only would have sufficed for such a change, and for your taking courage. Therefore gaze on me; I too was once in your state of mind, especially so; I had a burning zeal for the Law; yet afterwards I feared not to abandon the Law, to withdraw from that rule of life. And this you know full well how obstinately I clung hold of Judaism, and how with yet greater force I let it go. He does well to place this last in order: for most men, though they are given a thousand reasons, and those just ones, are more readily influenced by that which is like their own case, and more firmly hold to that which they see done by others.

Q: But, how do we that Paul was rebuking them for observing the Mosaic Law and not something else?
A:We don't know with 100% certainty, but the context of Galatians strongly suggests that Paul is referring to the Mosaic Law. He talks about it A LOT, noting how it doesn't need to be followed anymore.

(Galatains 5:2) Behold, I Paul tell you, that if you be circumcised, Christ shall profit you nothing.
(Galatians 6:12) For as many as desire to please in the flesh, they constrain you to be circumcised, only that they may not suffer the persecution of the cross of Christ.
(Galatians 4:4-5) But when the fulness  of the time was come, God sent his Son, made of a woman, made under the law: That he might redeem them who were under the law: that we might receive the adoption of sons 
(Galatians 3:24-25) Wherefore the law WAS our pedagogue in Christ, that we might be justified by faith. But after the faith is come, we are no longer under a pedagogue.

