Answer: Unfortunately, two feet is rather narrow for most shrubs. You might be able to train yew or a euonymous such as Manhattan to the dimensions you need.
The privet could also be renovated without too much trouble, and March would be the time to do that. Cut it off at the base and allow it to resprout from the roots. Shear it off by an inch or so neatly every time it grows about six to twelve inches to encourage additional branching. Shear the sides as needed to keep them growing at an angle, the angle starting wide at the base and narrowing as you go upward. This sort of triangular shaped hedge will allow sun to reach the base and keep it dense all the way down. Two feet would be a bit narrow for the privet, however.
Another alternative might be to install a solid fence or trellis panels about four feet high and stain it a soft mossy green and then allow clematis or other light weight vines to adorn it and provide summer color. The fence would be better in some ways for the flowers in the beds because hedges tend to be very greedy in terms of stealing moisture and nutrients from neighboring plants.
I hope this gives you some ideas.
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