It all comes down to being unevenly yoked...
I quote this first because this is key.
I almost asked the OP early on if he truly believed this passage to mean he shouldn't date her. If you believe this, then I think the discussion should be over, you just need to let God help you put out the little flame for this girl from a relationship standpoint.
If you don't believe this, then we can debate all day long.
I don't see any reason not to date her. If you both love each other and respect each other's beliefs (which seems to be the case, if she avoids taking His name in vain etc. around you), you won't be "unequally yoked." The Greek work translated as "unequally" in Corinthians is seen only once elsewhere in the Bible; in the book of Leviticus, the Lord tells us not to "unequally yoke" an ox and an ass since this would cause them to fall down. The danger is if you judge her (for that is the Lord's place, not ours), or if she cannot accept your faith, and thus you become yoked unequally, so that you cannot stand together because you end up resenting each other or your differences interfere with your Love (Love being, as Christ says, the fulfillment of the law).
The problem here, is who is to say she won't later?
Who is to say she isn't putting on an act at the moment to net the OP? Not cursing around someone is a far step from accepting a faith. If she can accept his faith then, why hasn't she?
Is not the passage in Leviticus directly speaking of not yoking one "breed" with another? Two totally different animals? It didn't say don't yoke a strong ox with a weak ox. It said don't yoke an ox with an ass. One faith with another? I'm not sure if it helps your case.
This is of course up to interpretation but please, read the context in Corinthians, I think reading the context is abundantly clear:
Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? What harmony is there between Christ and Belial? Or what does a believer have in common with an unbeliever? What agreement is there between the temple of God and idols? For we are the temple of the living God.
I see nowhere that talks of JUDGING or "if she can accept it"... It says: DON'T DO IT.
Where do any of those citations say it is beyond forgiveness?
Nobody said that sex outside of marriage is beyond forgiveness.
What's Romans 6 say of this?
What shall we say, then? Shall we go on sinning so that grace may increase? By no means!
We have DIED to sin, we shouldn't be RULED BY it, it should not be our MASTER, even if we are forgiven from it.
My personal opinion of sex is while a quick tongue might lie, sex is something that can be avoided. Keep boundaries and you'll not have a problem with it. Don't snuggle up and get handsy during a romance movie on the couch at home alone, in other words.
which is why Paul's Epistles to the Corinthians provide much more concrete and rigid rules than are often found in the rest of the NT.
By all means, since they are more strict than we'd like, we should throw them out.
I just know I've seen too many relationships that would've been a lot better with the wife providing spiritual guidance instead of the husband; I've seen a few fathers as spiritual leaders drive their children away from the faith with their words and deeds, when I honestly don't believe their mothers would have.
Which is why mate-selection among women is just as poor as it is among men. In both cases, STRONG CHRISTIANS need to be chosen, else you create the problem you described above. This is compounded when marrying nonbelievers.
if you should be basing a relationship on feelings that may very well be leading you away from HIM.
Very good point.
To put it bluntly: Satan is a very smart bastard.
Present the gospel, what a lovely thought, and scare her away, mess up ypur life, take a way a chance for God to do something
If distancing yourself from this girl on a relationship messes up his life then he has other issues than sharing the gospel

It's also an extremely arrogant statement to say what God's will is in this situation, especially when his written will (Bible) is quite clear on the subject.