I agree that no person can will himself saved;
Thanks for clarifying, and the above is biblical. We should then not deviate from this great truth in our further elaborations, but consistently apply it throughout our Gospel.
but I believe that a person can accept or reject God's invitation
I don't see any non-believer falling into being called (bid, invited) as are the elect per Scriptures example. If so, they would by necessity also have to be foreknown, predestined, called, justified, glorified Romans 8:29-30, as we see this word called only referring to the elect with all the other parts of the chain of redemption included. That is the biblical doctrine of effectual calling as revealed in the Gospel. Thus they are not called in this same manner in the chain of redemption.
We also see this truth expressed in Matthew 11:25-31, God revealing to whom he will, as well the Son, then calling them. I see him then revealing to those he desires to save, and these all come to him. In fact, all the Father has given him will come to him.
Therefore the receiving is really not what clinches salvation, is it? It is not by choice or will, as we agree, so we must apply that consistently. It is the effectual call that saves, not based on choice or determinative will of man, John 1:13, Romans 9:16. James 1:18.
I see nowhere in Scripture where God opens the heart, grants faith and repentance, and revelation, and then the person rejects that ultimately. Lydia is one example, and I see no counter example to this.
which I believe is extended to all.
Yes, I as well, in that it is both effectual and general.