Answer: It is not usually possible to cut back arborvitae the drastic way you wish to do it. The reason is that the old woody part of the plant does not regrow the way a yew or boxwood can. Instead it stays bare and looks pretty bad. It might also kill them outright. Since they are so overgrown it is probably better to replace them with something else that would mature in the three foot size range that you really need, or adapt your plan to include them at their current size. You can maintain them at the size they are by carefully reaching into the plant and removing the longest branch tips. I'm sorry I can't be more encouraging on that.
The bare side from being next to the fence may be able to grow in response to finally receiving light and air. I would wait until next spring and see how they do. It will take a long time for them to regain a symmetrical shape however, these are not very fast growers.
I hope this answers your question.
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