Can the cowling envelope the entire muffler without it giving room for the exhaust to get out? I know it looks aesthetically better but not sure about its practicality....

No.

I have seen the muffler entirely inside the cowl except for the outlet. There's an awful lot of heat released from the muffler

I have run the exhaust through the fuse and out just in front of the tail wheel. I still had to have some of the cowl cut to cool the engine. Sure made the plane quiet and easy to clean.

David