I've tried something like this and achieved mixed results. Instead of growing from the new high point, my citrus continued to grow from the tip but produced deformed looking leaves. My preferred technique is to wait for the next flush and pick off the new leaf buds at the tips so all the energy is directed to the lower, interior leaf buds.

You might enjoy investigating espalier and pleaching techniques.

Thank you for the detailed information @bonsai. I am really on the fence about whether I should try tying down the long branches, clipping the offending parts (and risk damaging my tree by losing leaves and limiting this year's crop), and just leaving it alone. I get frustrated whenever I look at it, which is opposite my goals for gardening. Should I change, or should I change the tree?.....

I couldn't post a photo as for some reason the correct folder won't open through houzz, but I had a similar problem branch. If I were in your situation I would do 2 things. 1. Amend my expectations. This doesn't mean give up entirely, but you won't get everything you want, so pick what's more important. 2. I'd keep the branch. But here's how. I would wrap it in wire or tie the tip to some twine and pull it around into that bare spot in the front of the tree. Over this growing season it will branch out upwards (remember apical dominance). I'd leave it over this growing season and evaluate next year. You won't lose any fruiting wood that way, and it will give you some time to decide. After it has branched and grown new foliage and after you have your fruit for the year, you can then revisit removing the branch. At that point you may decide that, yes it needs to go. Or, no, you actually kind of like it.

When it comes to trees you only have so much control. You can't make a bent and windswept tree into the perfect specimen of a straight trunk style, but you can make a beautiful windswept. Work with what you have, not what you want, and amend your expectations within the bounds of your tree. From there you might find you actually love what came out of it.

"Work with what you have, not what you want" is great advice for citrus growers, and life generally.

Citrus tree are very hard to grow what you want. Branches I don't want get broken but not killed. The branches provide for the tree until the tree discards them.

Great advice all. Modifying my expectations is probably easier than getting these trees to do what I want. I think Silica has mentioned elsewhere that the average life of a citrus tree in a container is 2 years (due to grower error, not inherent limitations of the cultivar). I've only been doing this for 2-3 years, so I need to remind myself that it's okay I haven't figured out how to keep my citrus happy yet. I keep thinking I've finally learned how to properly water them and then I'll lose half the leaves because I watered it twice a week in the summer. The it will get a new flush and I'm all excited but the leaves get completely mangled by miners and I couldn't spray because it was 110 degrees. Then I get through summer and it starts to get a fall flush but it's all at the tips and does nothing to fill out the empty middle. And it just goes on the same way every season. I will stop looking at pictures of happy citrus, lower my expectations, and keep trying. There, rant over.

@Steve, how does breaking the branches work? Is this all about apical dominance, like in grafting? It would seem if the energy from the leaves can still flow to the roots, then the tree should still be able to support new growth at the end, but it doesn't?

Basically, Steve and bonsai are suggesting the same thing, but one is breaking the branch and the other is bending it. I think I will try this. I just reported this into a new mix last week, will bending/breaking the branch cause too much stress for the tree?

Let me clear this up. My tree is much bigger and I am breaking the limbs that should be removed. I will then let the tree finish using them up and do the final discarding.

The limb in the box is a bad limb and should be removed. It is so big that cutting it off would adversely affect the roots on that side of the tree. It is also to big and long to break it over so I cut it half way up and bent over the branch lets. It will be safe to remove the limb in a year as long as I keep this limb on the north side of the tree to ween it from the tree.

The limb to be removed was a water sprout with a large space between leaves on a seed grown tree. The limb would not reach fruiting size until it would be 5 feet tall so the limb gets removed. You probably do not want to cut and break your limbs.

I think breaking the limbs might, but bending them shouldn't. You aren't actually harming the tree when you bend it, just simulating the bend that would occur naturally in the branches if it had set heavy fruit.

That makes so much sense, thank you Steve and bonsai!