I love what you've done in ppv2, really livened up my desire to play Osu!.
Here's my suggestion:

Allow sorting maps by Level as found on the osu!tp site. This level sorting should also factor in the currently selected mods.
In addition the aim and speed stats should be presented.
Thirdly the TP, or unmodified PP value should be displayed along with score.
We've all been in the position where we felt we had just scored a really good play but didn't get as much PP for it as we expected, and these changes should alleviate this problem.
End play:

This small change would give players insight as to the worth of their last play.
Didn't make a picture for it but the on the website, the user page should include modified PP rewards and perhaps also unmodified TP scores for best plays, and potentially include more than 10 maps as well.
I understand the reluctance to add a second 'scoring' method in addition to the already implemented scores, but to some extent I think it's not necessarily a bad thing. I'm sure many players already sneak peek at osu!tp website to get an idea of which maps to play and what they can expect from maps in terms of PP. These changes just integrate them into the Osu! client, with even more information.