The fireplace you have looks to be a masonry fireplace with aftermarket glass doors. The fireplace is between a negative ten and a positive five percent efficient. The doors cut down on heat loss. Close the doors when you are letting the fire die down to minimize the loss of air from the house via the chimney.

Cutting the legs on the grate will do very little to increase performance.

To get heat you need to modify the burning format. Adding an insert (wood, gas, or pellet) is the best and most expensive choice. If you want to heat a zone in your home this is the most efficient choice. Inserts will increase the heating performance to an efficiency range of 50 to 75%.
Good luck and happy heating.

If I understand fireplaces, the kind you have, which I had, is not meant to heat a house, it is more decorative. I replaced mine with an insert with blower. We just built our first fire of the year. Downstairs was 62, it is now 73 with blower full blast. It was the best investment we have ever made on a house. It saves money on wood, less gas bill, and good for the environment.

Your brick and mantle are pretty in my opinion.

Consider doing a search on this forum for direct vent. There are several lengthy posts on the subject that describe the advantages of such a system.