Agree, instead to remove entirely the Poncirus trunks, graft four citrus of similar vigour in the same tree. Much more useful and satisfying in a small space. You could have an early orange and a late season orange for example in the same tree. You can make good use of the extant trunks and graft it high also. Just cut the thorns (or alternatively keep it if there are rabbits or other herviborous animals in the area). Is easy to identify and keep trifoliate buds at bay, and keeping a part of the Poncirus would promote less suckering than chop it near the soil.
If you want two oranges, expect seeds unless you graft navel oranges.
The remaining tree has the narrow wings in the petiole common in lemons