If I were you, I would only thin out the fruits instead of pruning the tree. Remove the fruits from the outermost area of the canopy, remove from the outermost limbs of the thin branches. This will help your branches carry the remaining fruits and more so if they are closer to the trunk. Your fruits would be bigger and better quality compared to thinning them out by pruning.

Citrus trees tend to develop skirt (lower canopy) around its trunk to protect it from sunlight burns, and usually the skirts are only pruned to prevent it from touching the ground.

Citruses are usually not pruned unless if the time comes when you value structure more than fruit production. You prune when the tree shape doesn't suit your style, or some branches are diseased, touching the fences or house and other structures or interferes with other things for one reason or another. But if you do prune, do it in late spring to early summer. You need all the canopy you can use to tide over the winter. And should occasional frost drops by for a visit, your tree is more protected. And if some branches die off, which usually are the uppermost, you shouldn't remove them until the dangers of frosts are over. During the winter, you would need those dead branches for added cold protection just in case. You will know for sure which branches have surely died and will not recover by late spring to early summer, that is why you prune at that time to remove the dead branches. Plus, never prune when there are rains coming as it could make your tree susceptible to diseases. Late spring to early summer, usually is a lot drier than fall and winter. So that's another incentive to prune at that time should you really need to prune your citrus tree.

I for one seldom prune my tree, but for balancing it, I simply graft more cultivars to it like shown in the link here:

The ultimate multi-grafted citrus tree

I did some pruning on my Valencia orange last month. But it was only to keep lower branches from touching the ground. The branches I took away did have some fruit on them. Like joereal, I tend not to prune citrus very much. That is one nice big mandarin tree by the way.

On the other hand, I screwed up on my persimmon tree this season. It had hundreds of fruits (for the first time) and some of the branches tore away from the trunk due to the weight. Live and learn. Persimmon fuit are heavy.

WOW! Skrip, your tree is so healthy, despite the frost and the drought! And joereal, you are my hero. My citrus trees take up too much space (two were both supposed to be "dwarf" varieties when purchased) and so I have butchered them into lollipops, and I trim them all year long whenever the mood suits me. I still can't make use of all of the fruit. I pull 3/4 of the fruit off of my Oro Blanco grapefruit tree every year because it is far too productive and the branches break. My husband noticed ten grapefruit hanging on the end of a single branch this year, and quipped "this, I suppose, is why they call them GRAPE fruit."
I would love to graft some lemon branches onto my Bearss Lime, but the tree is shy of branches only on the north side, and I am afraid the grafts would not take well enough, what with the Santa Anas and the lack of sunlight. Should I tear it out and plant a lemon and a lime in the same hole, with east/ west orientation?

hosenemesis, based on my experience, Bearss lime don't graft very well on lemons. Best to plant them in one hole if you can find the same type rootstock or you can buy a sour orange and graft both of them