How long does it take to recruit research participants?
To answer your question on a recruitment phase. I would say — and this is just by the seat of my pants — you need to allow a good two to three months for a recruitment phase, if there's really a solid plan.
How long should UX research take?
The average research project—across all project types takes 42 days. On average, “discovery” projects (60 days) take twice as long as evaluative projects (28 days). When asked about a recent project, 63.1% of research said they had "Just Enough Time." 22.4% had "Not Enough" and only 14.6% had "More than Enough."