You're answering every question except the one I'm asking
Because everything you've said and the pictures you've posted lead me to believe that the problem you're having is not because of high rainfall in your area.
Your big issue is establishing grass in that section around your house. You've managed to get the grass seed to establish in other areas of your lawn, that receive the same amount of rain, even though you planted a grass seed that does not typically do well in your climate and you planted it at the peak of summer which is the worst time to plant a cool season lawn.
The issue you're having is clearly something localized to the area you're having problems with. People manage to grow grass successfully in areas with as much rain as you get. It's not like Georgia is devoid of lawns and you're the first one to ever try and plant grass seed nor the first one to try and plant KBG. I get a similar amount of rain and people in my area don't have problems getting grass seed to grow.
The house has been here since 1941 with no gutters. I added gutters
after I saw that grass wouldn't grow with the flow from the roof.
This explains a lot! All the problems you ascribe to heavy rain fall... leaching of nitrogen, calcium and other nutrients, compaction, etc.... multiply them many times over. That's what's happening around the perimeter of your home.
To give you an idea why... assume you had a 20' x 50' home with the roof covering 1,000 sq ft of ground. You'd have 140 linear feet perimeter.
If it rained 1" you'd have close to 625 gallons of water falling on your roof. That water sheets off your roof and lets assume sprays over a 1' wide path along the perimeter of your home (assume it's equal to make the math easier, some parts may get more or less depending on your roof design.) 625 gallons divided by the 140 sq ft perimeter means you have about 4.5 gallons of water per square foot hitting the soil around your house with every inch of rain.
In the open areas of your yard the soil will only get about 0.625 gallons of water per inch of rain. The area around your home is getting about 7 times that and it's not simply little droplets it's pouring on it. The force of the water likely severely compacted your clay soil around your house.
Without knowing the design of your roof and how far the water was actually coming down from the roof the numbers aren't accurate and I don't mean them to be anything other than an example to illustrate that without gutters the soil around your home received considerably more rain per square foot than other areas of your lawn.
It is clear from the photos that the soil around your house is very poorly draining resulting in a lot of standing water when it rains. You need to address those drainage issues. Not only to get grass to grow but because it's a nuisance and potentially damaging to the house structure to have that much water pooling there.
Even if someone were to answer your question regarding keeping the seed in place during heavy downpours when the area gets flooded, the issues with the poor drainage would lead to other problems once your lawn was established. You need to deal with the drainage and soil issues if you want to have healthy lawn growing in those areas. Even if you were to put sod down the excessive water and poor draining soil would eventually damage it.
In addition to dealing with the drainage issues I would recommend sending a sample of soil from that area to your local extension office for analysis because there are probably significant deficiencies in the soil due to how much water it received compared to other parts of your yard.
This is the only answer I can come up with (other than to plant swamp grass) as far as why you're grass isn't growing in that area based on the information you provided. Other issues such as too much sun and heat (plus what's reflected from the white siding). It's interesting that the pictures you took show that there is no grass in the areas of your houses shadow. That could be a factor but poor drainage is a big problem.
You don't seem to be happy with it so maybe someone else will come along and provide a different answer.