I'd say 'speech' rather than 'monologue'. 'Monologue' is generally used to make a contrast with 'dialogue' or 'conversation'. It is a term used in drama, lcinema and so on. The point here isn't that the words were spoken by one person, but rather that they were prepared beforehand. For that reason, 'speech' is preferable. He'd been rehearsing his speech He'd been practising his speech (GB spelling).

I would say that "rehearsing" and "practicing" are both correct in this context.

This is all fascinating. From the point of view of human behaviour, I think most people in this situation would "rehearse a dialogue". If someone is so careful as to prepare in advance what he should say, would he be so naive as to believe that after his "monologue" the situation or human interaction would abruptly end, or no one would say a word that would require his further response? It is more likely that he will prepare for the complete scenario. You would, wouldn't you? Iris, please note that "rehearse" includes the meaning (or definition) of "mentally prepare or recite" in addition to "practise" and is therefore a more useful verb in this instance, giving a wider scope that is more conducive to the description of a more realistic scenario.