I'm generally not in favor of solar chargers for their expense and they need a regulator (despite what people say), and as Mickz said, the sun can be unreliable (and the panel must face the sun etc).
In this case though it might help. (Depends on discharge-recharge cycle.)
You really need to look at battery specs and compare to your system to determine a size, but it might be reasonable to assume almost double the charge rate for a doubling in size.
But I think a cranking battery is the better choice - provided it is not discharged past 80% (20% DOD) - it should charge faster than a deep-cycle, else at least tolerate the short-fast charge better.
The Yuasa NP was merely an example, and an economical one for 7AH.
But 15AH generally is considerably more - eg 3x the price for only twice the capacity. Maybe 38AH or larger is more economical wrt AH per $ and - providing it is reasonable charged - should [I]live/I] longer - ie, its DOD won't be as big, and it should recover that lost charge quicker (the bigger, the better as they say...).
Alas there are still so many variables...