I'm contemplating some drainage projects this summer and spring and therefore I'm in tune with some of the calculations necessary for drainage.
I want to comment about your front drainage situation. It seems like the slope is going the wrong way. If it's indeed a 10% slope toward the house, then, I believe, dealing with the gutters ONLY is not going to solve your problem.
The dry well calculations are surprising. Just to drain about a 25' x 30' roof area I would need at least two barrels. You also need to provide a relief.
In your case, since water doesn't flow uphill your going to have to provide a passive overflow for the barrel. You may also have to provide it some distance away.
When you do, you can use corrogated pipe or ezflow pipe. The ezflow stuff doesn't require 6" of rock or fabric. The fabric is built in. Pipe needs to be pitched at 2-3% for remaining water to be able to seep back into the ground after being discharged through a pop-up or regular emitter. See
Drainage, Drip Irrigation, and Water Management Solutions - NDS Estimated cost is about $4/ft in 10' lengths. I think it beats the rock method hands down.
What you may require is a foundation drain along your foundation, such as the ESR-1107 from
Prefabricated Drainage Systems - Roof Drainage Products, Yard Drainage Solutions | American Wick Drain. I believe this product is available at Lowe's. The ESR-1107 can basically be described as an egg carton covered with filter fabric.
The sump method sounds like a decent idea for you. I'd put the overflow some distance away in case the pump failed.
Although, I haven't worked out prices and all of the details and verification of availability I talked to a nearby distributer (20 miles) of the Ezflow stuff.
Lowe's carries some of the ndspro line in the store. I don't know if it can be special ordered.
As I said I'm planning a major passive surface drainage project. It's probably going to be about 120' in two stages. I'm also "planning" to install tracer wire.