Help with eCalc and optimal kV - 5" Quad at 4s

Hello and thanks in advance for any help with this. I am building a quad that is using a pretty unconventional frame. The frame is physically limiting me to 5" props with a take off weight of about 1000 grams before batteries. I already learned that my current 3s battery (two 3s 2800 30c in parallel, cells are Molicel P28A) was not enough to generate thrust after the voltage drop so have proposed going up to 4s. While inputting 4s batteries into eCalc, I noticed my kV is a bit low for such small props (2204 - 2300kV). Playing with the trade offs between battery capacity/weight and higher kV, within my size constraints, I cannot break the 10 minute flight time mark. I was optimally trying to reach much longer flight times but am beginning to believe this by nature may only be possible with low kV motors swinging big props. Is this the case or is there a better configuration than what I am finding? This has been my best setup I could achieve thus far, yielding just over a 2.1 TTW ratio and 7.5 min flight timeā€¦

                  **Model Weight:**

1000g w/o Battery
1300-1450g with batteries

             	**Frame Size:**

370 mm - Motors are really mounted at 210mm making anything larger than 5" his the avionics

            **Battery Cell**	 	

LiPo 2700mAh - 25/35C

Configuration:

4 S 2 P Cell Capacity: 2700mAh
5400mAh total

              **ESC**

max 50A

              **Motor**

Mamba System

Toka 2306.5-2650 (2650)

            **Propeller**

Diameter:
5 inch Pitch:3.2 inch
# Blades:3