Correct commas in a long sentence ?

This is from an official document about determination in a Tribunal in UK.

So, this should be grammatically correct, at least mostly if not perfect.

However, I suspect misuses of commas.

1. One whole pargraph is only a single sentence as follows.

First we conclude, by reason of our general findings above that even though the Adjudicator's conclusion, that membership of the Falun Gong comprised within the terms of the 1951 Convention a particular social group, or as the Adjudicator actually put it a "social group," is an error, and indeed an error of law, it is not a material error, because activity for Falun Gong can on appropriate facts engage the alternative 1951 Convention reason of imputed political opinon.

2. To help you, I put some marks to show the sentence structure as follows:

The same color for the related clause, and paratheses for an inserted adverb phrase or clause were used.

First we conclude, (by reason of our general findings above) that even though the Adjudicator's conclusion, that membership of the Falun Gong comprised (within the terms of the 1951 Convention) a particular social group, or (as the Adjudicator actually put it) a "social group, " is an error, and indeed an error of law, it is not a material error, because activity for Falun Gong can on appropriate facts engage the alternative 1951 Convention reason of imputed political opinon.





and commas around an inserted phrase or clase, am I correct?



3. My changes about commas are as follows, correct me if I am wrong.

First, we conclude (, by reason of our general findings above,) that even though the Adjudicator's conclusion that membership of the Falun Gong comprised (, within the terms of the 1951 Convention, ) a particular social group, or (, as the Adjudicator actually put it,) a "social group," is an error, and indeed an error of law, it is not a material error, because activity for Falun Gong can on appropriate facts engage the alternative 1951 Convention reason of imputed political opinon.

4. I removed parentheses.

First, we conclude, by reason of our general findings above, that even though the Adjudicator's conclusion that membership of the Falun Gong comprised, within the terms of the 1951 Convention, a particular social group, or , as the Adjudicator actually put it, a "social group," is an error, and indeed an error of law, it is not a material error, because activity for Falun Gong can on appropriate facts engage the alternative 1951 Convention reason of imputed political opinon.

Thansk for help in advance.