OK, it's good that you have plenty of water depth!
The 60 cm Driver should be OK on your nTrance, but I'm not
sure that this fin has the flex chracteristics to make it really
good for "fin pumping" to get on plane early.
I'm familiar with the CR-12 and that should be pretty good with your 7.0 Solo.
As far as the weight of the board "affecting" early planing, yes, there is a difference,
and the lighter and wider the board, the more likely it is to plane up very early.
As I suggested earlier, the Bic formula board will be the earliest to plane, but as a
true formula style board, you give up some easy jibing and speed on a beam to close
reach as the formula boards are really designed for formula (upwind/downwind) racing, and while pretty good on more "reaching" points of sail, they are not as easy and forgiving as the Futura.
Also, if you have some chop to deal with as the wind speed increases, the Futura will remain easy to sail where the formula board may become a handful more quickly.
Unfortunately, the only way for you to really figure this out is to spend some time on each of these boards.
It's difficult to suggest "just the right board" as there are so many variables.
I'll stick with my earlier suggestion on the Futura 155 as being the board with the widest range of use for what you have suggested are your conditions.
If early to plane is the "holy grail" here, then look at formula boards or perhaps an Apollo.
If you want reasonably early planing, easy to sail, and very forgiving overall, then the Futura 155.
Whichever you choose you are going to have a short "learning curve" to transition to a bit different way of sailing.
Once past the "getting acquainted" sessions, you can work to advance your pumping skills to bring your planing threshold down even further.
Hope this helps,