Bridge-grafting, and all other grafting, is done just as the tree breaks dormancy.  Fruit trees are in their highest growth period at this time.  Once they flower, and now grow fruit, the energy of the tree is diverted into fruit production, not into vegetative growth.

It would be quite risky to try and graft your tree now, but if you think the tree is in decline because of the girdling, you might try it, knowing that it might not work at all and you could further damage the trunk.

At the least, you could put rabbit wire around the trunk, make sure it's impermeable for rodents to get to the trunk in the winter, and try a graft in the spring.

Keep watering the tree now and with winter watering to maximize the chances of success.

Here is a detailed description of how to collect the scion wood, keep it from sprouting and then doing the grafting:

https://extension.wvu.edu/agriculture/horticulture/bridge-grafting

Thank you, this is super helpful. When in spring would you recommend doing the graft? I live in Denver. 



As with anything in agriculture, grafting is weather dependent.

The best time is usually in April or early May when the flower buds are beginning to open up until flower full opening.  Scion wood for the grafts can be taken in late winter/early spring and put into cold storage (refrigerator) so that it doesn't produce blossoms and remains dormant until the time of grafting.