I'm assuming you have the 26 inch hard case. That is what I have. I also have 700C wheels.

I find it impossible to get the hard case closed with the tires on the rims. I've tried it several ways and still no dice. So, to save the trouble of trying any more, I simply remove the tires from the rims.

Why is removing the tires such a concern of yours? To get my bike into the box, I have to do a fair amunt of disassembly. Mounting the tires on the reassembled bike is one of the last things I do and it takes a few extra minutes. I am usually tired at that point in the assembly and sometimes I leave to the next day or a few hours later. But, it isn't such a big problem that I would select a tire based primarily on whether or not if fit into my bike box without being dismounted.