I still don’t understand what you mean by the “two-part research experience” and an optional second part. McNair is a federally funded TRIO program that has to adhere to certain program characteristics in order for universities to get and maintain their funding. Opportunities for research experience with professors is one of those required components (https://www2.ed.gov/programs/triomcnair/index.html). A mentored research experience with a faculty member is THE core component of the program. The program is concerned with getting underrepresented students into graduate school, and research experience is a key component of doctoral admissions. The faculty-mentored research is quite literally the point, and in my experience with the McNair programs I am familiar with, it is not optional. I also perused the website with the listing of McNair programs. Not all have websites, but of the ones that do I was unable to find a single one that doesn’t require a mentored research experience.
So I’m a little confused when you say you were a McNair Scholar but also didn’t get much research experience. It’s not that I don’t believe you, but rather I’m wondering about the structure and quality of the McNair program you participated in and how they’ve managed to maintain their funding without providing you with a literally required part of the curriculum.
That’s neither here nor there now, though. What exactly did you do for research, and how long? What, exactly, does the “first part” of being a McNair scholar at your institution consist of?
Also, what are your career goals for this PhD? While you are absolutely right to favor program fit over ranking, ranking/reputation should still be a factor in your search. If academia is your goal, note that program reputation within your field has a huge impact on the kind of place you end up at. It’s a general rule of thumb that you can teach at schools 1+ tier(s) below the one where you got your PhD. Even if industry is your goal, the reputation of your program within your (sub)field can matter. That doesn’t mean you have to go to a tippy-top school, but you do want a well-respected one. However, if you are just doing this because you really love school and you want to continue going, then it really doesn’t matter as much.
However, even a T2 or T3 program is going to want to see some research experience. For most research programs an undergraduate thesis alone isn’t sufficient, but if yours was really two years of research done alongside a professor and your thesis is outstanding, that might work out. Simply expressing your genuine interest and reasoning for wanting a PhD isn’t enough on its own; most programs want to know that you know what you’re signing yourself up for for 5-6+ years. They’ll want evidence that you were successful at research before. If your undergraduate thesis was outstanding, then maybe some of the T3/T4 programs will show some interest, but I do think this may be an uphill battle - particularly with borderline GRE scores.
Getting a PhD isn’t really a box you can check on a specific “timeline.” First of all, as I mentioned, program reputation is important for job placement. In most cases, it’s better for a student in the long run if they wait 2-3 years and go to a better-reputed program than it is for them to go to a low-ranked program right away. It’s not just about job placement, either; students at top programs tend to get more funding, more publications, and are more competitive for national fellowships and scholarships. Part of that is selection bias, but part of it is the infrastructure and support that exists at top programs. (That’s not even to mention the fact that PhDs frequently take longer, and sometimes much longer, than people anticipate.)
Can you say more about why it is vital to you to stick to a specific timeline? In the long run, 2 years isn’t very long at all.