Perhaps it is Tecoma x âÂÂOrange JubileeâÂÂ

Here is a link that might be useful: orange jubilee

Thank you, that could be it.

Tecoma x smithii is a faster/larger growing orange flowered Tecoma, and I've also used it trained as a standard. It resists being kept to a single trunk, and needs constant pruning to keep it from reverting to a shrub.

Thank you, Bahia. 'Constant pruning' scares me away a bit, since I'm looking for something more low-maintenance.

For orange flowers, I'm also considering Salvia regla. We have one growing on the north side of our house where it gets morning sun in summer, and only bright shade in winter. It is very happy there. However, I'm wondering if it would be as happy with more sun, since even now in mid-October the spot I'm considering for it is still very sunny.

Can anyone recommend a limbed-up shrub or small tree with orange blooms that likes these conditions: east-facing with all-day summer sun, amended clay soil, low-to-moderate water).

You can't beat the Tecoma x smithii for dramatic and long season of blooms, but periodically you will need to prune out new basal shoots to keep as a standard. I've got one trained as a standard, and don't mind the occasional effort, but plant and forget use would be to allow this to grow as a large dense shrub.