May I suggest you also find a way to make your trunions of steel also, if you plan to fire this gun? And, the trunions have to be connected to the steel barrel, and not the wooden liner. Even firing blanks, these things generate some recoil forces, and the carriage has to be able to take them, as they pass from the barrel to the trunions. to the carriage, to the ground. you will split the wooden tongues of the carriage unless they are supported with iron or steel straps around the trunions, and that strapping goes around the front end of each tongue, and well back along the top edge, too.
I built a Light 6 pound British Field Piece with a friend, and we used green Oak lumber to make the tongue of the carriage, and pounded iron strapping that was 1/4 " thick to meet original specs, around the wood to protect the carriage from recoil. Please, do not treat these guns lightly, as they can come apart on you, even when the barrel liner remains intact. MY friend's cannon was made of cast steel, and had a 1/4" thick liner in addition to the casting. The liner was rated to take the entire load, pressure-wise. However, we spent a lot of time making that carriage to spec, and doing it right, so he could have the option of firing live rounds, including lead cannon balls, with the one pound of powder per shot load that was called for in the orginal military spec sheet. After we did that a couple of times, we found a cheaper way to fire that cannon, and still have fun.