Well, I hate to say it, but that frame is just not right for C5 set-up. The C5 frame has some serious "kick-up" in the front and rear. Your frame is straight. Your frame sits very high in relation to the suspension.
The bottom line is that the vette was designed to have the torque tube run through the body in a large center tunnel. The tunnel is so big that the exhaust fits in there too. It is 12" high measured from the C5 floorboards. The way yours is set-up the truck's floorboards are going to be sitting on top of that. So in relation to the vette body, your truck has at least a 12" body lift.
If you want the thing to sit low, there's no way around running the torque tube through the cab and loosing some bed space. Look at
Jay Leno's Toronado I couldn't find pics of the interior, but they ran a large tunnel in that thing.
You can drop the suspension using shockwaves in the stock shock location up front to eliminate the lateral leaf. In the rear I haven't found an airspring-over-shock (like shockwaves) that will fit in the stock shock location, but there are ways to mount it elsewhere.
One way is do use a push rod/rocker set-up like Porterbuilt did here:
Another option is to mount the shockwaves forward of the rear arms like this:
Those are some of your suspension options. I think you are going to have to make some serious changes to your chassis/body in order to get it low, regardless of what you do to the suspension. Look at the '61 in my sig link. My rockers actually sit lower than the vette's did without any suspension mods, and I still plan on running shockwaves.
I hope this is not discouraging for you to hear. Your truck has great potential if the right engineering is put into it. I'd be happy to provide you any other info, measurements, pics you might need.