What explains the different impression one gets reading Acts (Torah obedient) and Paul's letters (Torah negating)?  

Well, the author of Acts was Luke. In Luke 16, he quotes Jesus affirming the Torah continues, and is not abrogated. Luke quotes Jesus affirming the Law in many contexts, and faults the Pharisees for negating it. See my article Luke is a Non-Pauline Gospel. 

So Paul behaved around Luke who knew Jesus' position on the Law as one who adhered to it and perpetuated it. Luke was never made aware Paul did not truly believe the Law continued. Luke only heard Paul teach the Law continued.

So Paul spoke one way around Luke who knew Jesus affirmed the Law continues, and Paul spoke contrarily around others whom Paul knew they did not care whether the Law continues.   

This is not mere surmise, for Paul confesses this behavioral tactic.

This is what explains Paul's epistle to the Romans and many other places where Paul clearly negates the Law's ongoing validity.

Paul blatantly confesses that he pretends to be Law-compliant around those who think the Law  is still in effect, but around those who are not Law-compliant, Paul will live like the Law applies but truly only lives by the Law of Christ, i.e., apparently a euphemism for his conscience. I wrote an article on this: Guile in Paul. 

So I agree with the Messianics. I wish they could convince people Paul was sincerely Torah-observant, and did not obey from pretense. But when the crush of opposing verses comes upon them, there is only one solution that explains the self-contradiction: Paul openly avows he practiced "guile" -- a nice word for 'deception.'  Hence, the passages in Luke reflect what Paul allowed Luke to see. 

Pious Fraud Doctrine / Casuistry Doctrine in Roman Catholic Church

Paul is the basis of the "pious fraud" doctrine in the Catholic Church. This doctrine teaches, based upon Paul, that it is proper to use a so-called "pious" fraud to advance the gospel ... for the end justifies the means. See Charles Hodge, Systematic Theology (1871) at 448.

Paul many times affirms "all things are permissible, but not all things are expedient." Thus, based upon a morality of expedience, combined with Paul's view on using deception for Christ (see Guile in Paul), we see the pious fraud doctrine -- taught as the subject of Casuistry in Jesuit colleges until the modern era -- has a firm foundation in Paul's teachings. But for one who follows Christ, this must be repugnant. For Peter says, in Him was found "no guile." Jesus, not Paul, must be our example. 

And this same tactic appears often in Paul's epistle to the Romans where Paul begins by affirming the Law is good and no one will be justified who does not follow the Law. However, then Paul undercuts these statements by teaching the Law's nullification, and teaching justification is by faith imputing the Law's righteousness. This allows all the prior concessions -- which give the appearance of Law-adherence -- to fade into oblivion. The anti-Torah Paulinists are the ones reading Paul correctly. Yet, the Messianics are correct Paul speaks to the opposite position often.  

The truth is the Messianics are deluded by Paul's crafty deception -- a skill Paul encouraged and praised as his own practice -- incredibly enough.

Shalom and blessings,

Doug