As far as I understand all three alternatives, pro manko de tempo, pro tempomanko, and pro tempmanko, are correct. However, I wonder if there are any reasons for using one of them rather than the others? Or can I choose freely?
You can choose freely, the reasons for the choice will be most likely personal, such as how you first learned it, or how your native language works.
tempmanko I think should be limited to the written form, most people (Slavic peakers not included) will have a hard time pronouncing the consonant cluster.
tempomanko is just like the German construction Zeitnot, Esperanto is very similar to German in the way they allow and build compound words.
pro manko de tempo has appeal to speakers of languages that do not compound words as freely, compare with the Romanian din lipsă de timp, which is a word-by-word translation.