Did Paul teach that believers immediately go to heaven upon death?

Two texts that are often marshalled against Latter-day Saint theology vis-à-vis the “intermediate state” are 2 Cor 5:6-9 and Phil 1:23—critics usually cite these texts as “proof” that, after Christ's resurrection and ascension, believers immediately go to heaven upon death, not to the “spirit world” as Latter-day Saint theology affirms:

Therefore, we are always confident, knowing that, whilst we are home in the body, we are absent from the Lord: (for we walk by faith, not by sight :) We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord. Wherefore we labour, that whether present or absent, we may be accepted of him. (2 Cor 5:6-9)

For I am in a strait betwixt two, having a desire to depart, and to be with Christ; which is far better. (Phil 1:23)

The following comes from the recent book by J. Richard Middleton, A New Heaven and a New Earth: Reclaiming Biblical Eschatology (Baker Academic, 2014), pp. 230-31 that provides a pretty sound refutation of the popular misuse of these texts:

[On 2 Cor 5:6-9] The first thing we should note is how Paul has already stated in 5:1-2 that his actual hope is for the heavenly dwelling that God has prepared (the resurrection body), and in 5:3-4 he affirms that he does not want to be “naked” or “unclothed” (disembodied). And yet Paul says that he prefers to be away from the (present) body and at home with the Lord (5:8). Could Paul have contradictory hopes? . . .[W]e need to pay attention to Paul’s key statement near the end of chapter 4 about the basis of his hope even amid tribulations and suffering (vv.8-12). The reason why Paul says he can live faithfully in the midst of suffering is this: “We know that the one who raised the Lord Jesus will raise us also with Jesus, and will bring us with you into his presence”(v. 14). There is no separation here of resurrection and being with Christ. Not only does Paul look forward to the resurrection but he also conceives of being in a resurrected (embodied) state in the Lord’s presence. This means that when Paul comes to speak of being “at home with the Lord” in 5:8, there is no reason to separate this from his hope of resurrection (except that we are habituated to reading the text this way). Paul is not speaking of being with Christ immediately at death; rather, he is looking to the second coming, at which time we will be raised and be with Christ in the new creation. [On Phil 1:23] While interpreters often take Paul as expressing a preference for death . . . the text does not actually say that it would be immediate. Yes, he wants to be “with Christ,” but he does not elaborate on where or exactly when this will be. Once again, the rest of Scripture would lead us to expect that Paul is thinking of the eschaton. There is no clear teaching here of any interim state in heaven.