This has already been addressed in detail by me, if not by others. You, conveniently, do not continue on into Romans 8. Interested readers, please see post 51 for the details.
But I offer the following as a complementary argument to post 51. Here the end of Romans 7 and the beginning of Romans 8:
Wretched man that I am! Who will set me free from [r]the body of this death? 25 Thanks be to God through Jesus Christ our Lord! So then, on the one hand I myself with my mind am serving the law of God, but on the other, with my flesh the law of sin. Therefore there is now no condemnation for those who are in Christ Jesus. 2 For the law of the Spirit of life [a]in Christ Jesus has set you free from the law of sin and of death. 3 For what the Law could not do, weak as it was through the flesh, God did.....
Note the "wretched man I, yes, am". Present tense. You are arguing that from the use of the present tense in verse 25 ("I myself with my mind am serving the law of God"), we can infer the Law of Moses is still in force. Well, there is a problem with this. Is Paul still "wretched" at the end? Of course not! He has been set free from his wretched state. So here is the clincher: Even though Paul uses the present tense in declaring he is wretched, he does not want us to think he is still wretched. Likewise, we cannot assume that because he "serves the Law of God" - present tense - that he is still doing so by the time we get to Romans 8.
The use of the present tense is arguably confusing, but the overall logic of the passage places the Romans 7 stuff in the past.