Does anyone know where you can get a 240mm fan that might mount on the standard fittings of 4 x 120 mm fans?
To the best of my knowledge, there's no such fan. If there were one, it would need a circular exhaust very different from the four circular exhausts you already have. I suggest you abandon this quest.
You say you're interested in low noise, yet you indicate (as I understand it) that you're only using two fans in the four-fan slot. Do you realize that raises the noise level for your exhaust fans 15dBA? No, I'm not kidding.
Say you need 4X CFM for your case cooling. You can get X from each of 4 fans, or 2X from each of 2 fans. That means you need twice the RPM from the 2 fans as from the 4 - a difference of 18dBA! With twice as many fans you have 3dBA more noise, so the net noise level difference between 2 and 4 fans is 15dBA - a very substantial difference indeed.
Your computer, your choice(s).