Frustrated (LONG POST)

I was laid off in April, and began freelancing with a consultancy that serves a number of organizations in my former industry. My colleagues are great, my portfolio of clients is diverse and full of smart, passionate people. The job is fully remote for the foreseeable future, and likely to remain so for a while. There hasn't been enough work to be full time, but I consistently say yes when asked to join a new client team, so they have been offering me more to do and more responsibility. Still, due to COVID it hasn't been full time, so it's been a struggle financially. In July, a former colleague who I hadn't spoken with in over 10 years called to say she was retiring from a Director slot in the field we both worked in, and that she put my name forward for the job. I interviewed and was told I was their choice, but that there were some bureaucratic hurdles to clear before they could bring me on. The salary and title bump were significant, and I was excited to join the staff. That was July. I am not yet on staff. I have repeatedly requested updates, only to hear "it's not in our control." I met with personnel 8 weeks ago and was told to send my transcript and proof of my freelancing, which I did. Then silence. Last week, my future supervisor called in a tizzy that they need me on board right away because they have a big deadline due. I reminded her that I was waiting for THEM to approve me. There is no remote option, although my office is private and isolated. She then told me that the salary that I was quoted by HR was $7K more than what I was going to be paid. When I expressed my disappointment, her response was "Well, it's still a lot of money, and still more than you asked for." That's true, but (a) I am a single income household; (b) I have a child with special learning needs who I have to make arrangements for and (c) I have been without a steady income for six months because I was told I would be brought on board any day. It's like the right hand has no idea what the left is doing. This week, they finally called to schedule my physical, and I went in to meet unofficially with my coworker, who I've also known for 20 years. She and I went over the upcoming project and she gave me all the things I need to get started. I'm not officially on staff, but this is a heavy lift and it funds the whole program. If I don't do it, there is no one to do it, and it's due mid-December. All in all, I'm annoyed by the bureaucracy, and the lack of authority my supervisor seems to have makes me wonder how I'm going to get anything done. My friend who advanced me for the job has been curiously close-mouthed except to say "you get used to it." Recently, the consultancy offered me the chance to take the lead on a client, and I told them about this new position. They countered with more money, subsidized health benefits, and the promise of more responsibility, better title and more hours, still remote. I'm waiting for all the details, but my inclination is to take what the consultancy offers if it's better or comparable to the other job. It gives me more autonomy, and more diversity in the work I will be doing and skills I will be building. They pay for professional development and for bringing in new clients and offer a highly flexible approach to time off. I'm trying to keep an open mind about this job in case the consultancy does not come through (although I expect they will). Questions: Do I start the job I don't want, do the project and then resign? I want to give them lots of time to find a replacement, since their process takes so long. I am worried that the exit process will be as long as the entrance process. Or do I do the project gratis, turn it in and tell them I'm not starting? Do I tell them that their bureaucracy is why? And I am feeling bad about my friend and my colleague who are excited for me to run this program. But I am so deeply aggravated by the time this has taken and all the interactions I've had, and don't think it's the right work environment for me as I am now, even though it seemed like a great fit 6 months ago. I have a low tolerance for inefficiency. How do I break the news to her? Thanks all...I know this is long; it's all the stuff swirling in my head.