This is the challenge of doing commercial, not academic, research: Your stakeholders care less about rigor and process as they do about results and impact.

Do push back when you think the schedule is unrealistic but also be flexible with your approach. Yes, research takes time, but there are ways you can do "good enough" research that provides your stakeholder teams with the info they need so they can get unblocked and you can move on to the next thing. Rinse and repeat until you show enough impact and get sufficient buy-in to do it the "right" way.

Reading between the lines, I think there are a number of things you can compromise on that will give the teams what they need and give you what you need, which is to not be so overworked.

Timebox everything you do. They give you a month? Okay, first define and align on your recruitment criteria for your interviews. Start recruiting these right away, schedule for 2 weeks out. Don't go over board with the sample size, do ~5-8.

While recruitment is going on, schedule BRIEF stakeholder interviews to get their top 3 priorities or questions.

Can you get some resources to help with some of the logistic works, like recruitment and scheduling? Maybe someone at the company can help you 10 hours a week or maybe you can contract with a recruitment agency.

I’m talking about the fact that onboarding into a new B2B SaaS product, interviewing stakeholders, reviewing previous research/available customer data and deciding what method to use & recruiting participants, doing research, then analysis, workshops with stakeholders and preparing a report - all of that can take more than one month given that I am also working on other projects and need to attend many weekly meetings.

forced to produce something that will make me look bad in front of other people in the company.