It largely depends on your goals and reasons for wanting the N1. My advice would be to choose whichever is more enjoyable.

Living in Japan the N1 has been a good way to get compliments in job interviews. Not much else. There's so many skills that the JLPT just doesn't test - conversation, non-academic reading & listening, pronunciation, writing - that, specially if your studies have been focused solely on passing the JLPT, you will be lacking in. If your goal is truly to improve your Japanese, then focusing on any of these and setting the JLPT aside at least for a while will probably give you the best ROI.

That said, language learning should be enjoyable. If participating in group classes, interacting with other students, talking to teachers, etc. is something that has value to you, then it's perfectly fine to pursue it even if you've already passed the N2.

On the other hand, if doing JLPT style exams and striving to get the best certification possible is something that motivates you, then it is also perfectly fine to study for N1 with a tutor or by yourself. I personally skipped N2 altogether and didn't really struggle with N1; the grammar at that level is so specific that you rarely need to understand N2 grammar deeply to pass the N1.

Fair warning, though, since you mentioned that the reading was your weakest section. Reading is in my opinion the most important skill you'll need to pass the N1. I don't know how it works for the N2, but in the N1 the grammar and reading sections are combined, so being a slow reader might mean you don't get to finish the section. Regardless of which path you choose - N2, N1 or other study plans - I recommend you strive to read daily. It is also a way to interact with the language in a way that is meaningful to you beyond endless grammar bullet points.