Allan, I understand your point, but this is not the only reference to God's granting repentance.
Of this I am well aware.
First, Acts 5:30, God grants repentance to Israel.
Second, Acts 11:18 God grants repentance to the Gentiles, as well
Third, Paul expresses a desire that God might grant repentance to opponents of the Gospel.
While I agree with point 1 and 2, I think you are reading something into 3 that is not intended. The passage regarding point 3 is not fixated on or about God having to grant repentance as it's theme or main point.. but is more to the point of Paul was telling Timothy that while instruncting these people to know the truth, God might allow them to repent while he is engaging them. IOW - Paul is speaking the potential of him being used by God through or in meekness and correction toward those who misunderstand or don't know the truth of God - for the purpose of salvation.
Since we know, and both agree, that no man desires to know anything about God on his own, nor of/on his own will he come to God in repentance unless God first work on man. We also know there is no specific age at which God chooses to reveal His truths to anyone. Therefore it is our work as believers to spread the good news so that if God is working on them, they might come to salvation through your/our obedience toward God in sharing and correcting of His word with others. Thus you have in other places where Paul says much the same thing.. how will they know unless they hear.. and how will they hear unless someone is sent..ect.
I am not arguing the fact that God must grant these things, but to assume the term 'grant' means to give to someone what they did not have is, I believe, going beyond the text, the context, and intention of the author. And we have already established that God granting repentance was to the Nation Israel and to the Gentiles without any qualifier to show or allude to exclusion but more accurately, total inclussion.
However I think this is part of the problem between both groups. It is not necessarily the term grant.. but what it means or entails.
While the Reformed group says it (faith, repentance, ect..) is something God must give because it is not something they actaully have. -ie. like giving a kid a bike who does not have one.
While the other group believes God 'grants' as well, yet not in the sense that man does not have the capcity to do so but that his current fallen nature has blinded him to the truth making them useless. Therefore man has no knowledge that or what he needs to use them for regarding his salvation because he doesn't even know he needs saving. As such his ablity of faith or repentance toward God, is nullified or rendered uselss because they are unaware that they need to do anything of the sort. Thus God 'granting' is the giving of knowledge necessary to 'enable' what was useless prior.
Both believe God must grant, and that God enables, we just disagree on the mechanics and scriptures supporting eachs view. In fact we both hold to many of the same scripture to establish 'our' view.. that is what I find most humorous.
Now obviously, not every Jew repents; not every Gentile repents, and not every opponent of the gospel repents.
I will agree here, yet let us read the texts again..
..to give repentance to Israel..
..grants repentance to the Gentiles..
Exactly who is excluded in the giving of repentance here?
Note there is no such qualifier. The qualifier of whom God grants repentance is actually everyone in that group and does not say, allude to, or insinuate a sub-group within that group.
The third aspect you give, is not about God granting repentance (as the main idea or theme) but is secondary to us being obedient to God in reaching out to all men.. so that as we are obedient to Him, He might use our obedience to bring another to salvation as He grants them repentance. Don't misunderstand me though. I am not saying God doesn't allow/grant/give men repentance. If God did not work upon man, then no man would ever repent or even consider it an option. Thus repentance, according to scripture is given to all men, just not all at the same time
I find it note worthy that in 1 Tim 2:4 it tells us that God desires all men to be saved and come to the knowledge of truth. The context of this in preveous and following passages establish beyond all doubt the 'all' is inclusive and not exclusive. Paul doesn't switch gears and then is 2 Tim state only some, but is still expressing the same thing but with respect to individuals at various times and why we need to be proclaiming the word - to be used of God in the salvation of His elect.
But Peter, Paul, and the Jewish Christians in Jerusalem understood that for those who did, their ability to repent was given by God. And it seems also to me that with that ability also came the desire to repent.
Here is where you seem to be adding to the text 2 seperate assumptions.
The first assumption, is presuming 'ability' is something they did not have.
.. let me qualify this however. I agree that God must give them the ability to believe, but the distinction is what constitutes them obtaining said 'ability' - I'll explain further down.
And the second assumption is repentance is something like an object that is given to man and thus once he has it, he will then 'desire' to us it due to now having the abilty to repent.
To the first - just because a person does not know what a back flip is or that they can do a back flip, does not mean they do not have the ability.
But I will grant that ability, in a sense, is given/obtained once we have knowledge and with that are now able or maybe better, enabled to consider it or do it
Thus my point is that they did in fact have the ability to repent just as man does to believe/have faith, but without any undiluted knowedge (IOW- apart from us obtaining the knowledge ourselves) we will never know what to do or on whom to call, if anyone.
To the second assumption that repentance itself is something that must be given because we don't have it, and as I see it not biblical or contextual.
Men can repent of anything thus repentance, like faith is a natural condition within man. The issue is how they come to doing either in a godly manner (that is key and I know you agree). Of themselves no man will do either toward God because he does not know or care about the things of God. Thus it is God who must come to man and reveal Himself and spiritual truths to man, and it is in this sense, God gives them to man as now man is faced with the truth he never knew prior. Will he believe it or not and if so, repentance is what naturally follows.
Beyond all this, if for no other reason, we ought to pray for the lost because it is certainly biblical. Paul himself prayed the salvation of all Israel. If he can do it, so can, and should, we.
But see, here is where you have a disconnect with Pauls theology. If Paul taught, as you believe, that only the elect will be granted repentence and thus salvation.. you also state, with scripture, that Paul prayed for the salvation of all Isreal, the Jewish nation. That just doesn't fit his theology, and we would have to say he is mixed up on what he is teaching.