From your description, your problems lie in the fact the bores were never honed for the new rings and the rings have never seated. If the rings don't seat, they won't scrape the oil off of the cylinder walls, and will more or less act like a pump, pushing the oil further up into the combustion area, thus burning oil and creating the blue smoke.
I don't know the reason for the ring change in the first place, but you can't just put new rings in and expect them to work. There are several steps to ensure your the new rings actually work as well as tolerances to meet. Things like ring end gap, bore taper, piston to wall clearance, and more. When I talked about how the rings were clocked, if the orientation of the rings put the end gaps in line, it will hurt oil control and dynamic compression. There are a LOT of considerations.
I'd suggest your best bet is to take it all apart. Clean everything again. The new rings should still be useable, but you'll need to clock them correctly. You'll also want to ensure the ring gaps are not too big (or too small). Hone and thoroughly clean the cylinders, then put it all back together using new gaskets to seal it up (the old head gasket SHOULD NOT be reused). Once done, it should probably behave a lot better for you and not have the oil usage you're seeing now.