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Я (очень) сильно уставший ("чрезмерно" is not well-suited for this role. Also "Я (очень) сильно устал" is simplier and little more natural here)
но мне надо ("следует" is more like "should", not...

Both are correct.
However in first case "хотя бы" is applied to "мог", while in second case "хотя бы" is applied to "позвонить".
So... first one is better suitable for expressing idea, that he...

хотя бы - 1,2 (expressing wish of something to be done or to have some quality/quantity)
по крайней мере/как минимум - 1,2,3 (more universal, like 'at least')