Trunk cut?

[MaggieBlue2]

I have 2 washies that are about 5 years old...was told they were filifera but may be a filibusta. We live in the DFW area and they took a pretty bad hit in the freeze in February.  After the weather passed, the leaves were quite bleached (not crispy brown) due to the snow but nothing on the tree was collapsed which we took as a positive sign. Other than the frond color they looked completely normal. As the lower fronds drooped and no green spots were remaining, we would cut them. I periodically give them a tug to see if there is spear pull and they have been firm until 3 days ago. The spear came out but the end was still bright white and fleshy and no odor was noted. I put peroxide down the hole and put copper fungicide on the outside of the tree and surrounding soil. The hole is about a foot deep but you can see bright white flesh at the bottom with a flashlight and nothing appears to be rotting. I worry with no fronds and a hole that deep, the tree cannot photosynthesize adequately. Should the trunk be cut closer to the base of the hole? I still have green spots on some surrounding cut fronds so I prefer to be cautious but do not want to lose the tree. For now, I am putting just a little peroxide in the hole to keep it from rotting while not drowning in liquid and covering the hole with burlap overnight and during threat of rain. Any advice is appreciated.