I would think the Cork clay would do the trick.
First, is this fine silver? Because every type of metal clay is treated differently. You said the base is cork clay? It is really important that the cork clay is very dry all the way to the core before firing. That will keep it from trying to explode on you. When firing it ramp your kiln slower than normal to give the cork a chance to burn out. If the thickness of the clay is at least 1.25 mm it should not sag in firing. I would lay it on its back nose up, supported by either kiln wool, or vermiculite. I would fire it longer than the instructions say,. At least 2 hours. If it is Art Clay or PMC they are dense enough that you should be fine. I have fired 2 ounce boxes, and a large fish and they came out perfect. Just make sure the silver is thick enough.
I’m using EZ960 and it’s only about 1mm thick in some spots and where the “sheet” is folded over its 1.25mm so thickness is not consistent. Regarding the cork clay I was thinking of using that to fill the head and upper portion to hold the hollow form to fire and then mound the alumina or vermiculite to fill the lower portion. EZ960 is a full ramp to 1675 for 2 hours for recommended fire. Kiln wool is not recommended with this clay. Laying it on its back should work as the thinner areas of the “sheet” are actually on the back side. Thank you for the advice on this!
EZ 960 presents a special problem as everything seems to stick to it. Also the firing times are long. Try using kiln paper as a surface to lay the dog. I thought you had already used cork clay as a support to build your dog. You might be able to push some up there, but it is very firm. You may have better luck with paper clay in the white package. As it is softer and more malleable .
Do not use the black package paper clay as it is very similar to investment and will not burn out. I almost want to say to saw your dog in half, fire each side with a support, then put it together with clay and refire a second time. I have done this before with larger pieces, though I have no idea how large yours is. Best of luck