I don't believe keeping the organization as an LLC is best, but nor do I believe dissolving the LLC is appropriate, necessarily.
I would recommend converting your LLC to a corporation (which in some cases can be as easy as "checking a box" - see https://www.ftb.ca.gov/professionals/taxnews/2009/July/Article_10.shtml) - with the Secretary of State and FTB, and going from there. Also - remember that you'll need to also register with the California Attorney General.
Your question, however, is if the amended statement is acceptable for tax exemption - and the answer is yes. It's the standard boilerplate for charitable purpose. However, you do also need a statement regarding treatment of assets - that they won't inure to the benefit of any individual and that upon dissolution assets will only be distributed for charitable purposes (in California, they go even farther than that and restrict distribution to organizations recognized as exempt under the same 501(c) provision.)
As an aside - have you looked at converting to a Benefit or Flexible Purpose Corporation, instead of a nonprofit? That is another option to evaluate.
May L. Harris, J.D., M.A.
For Purpose Law Group, a PLC
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HI. I have worked with a lot of 501(c)(3)'s in the past on the Form 1023s. Unfortunately, it is very difficult to get tax-exempt status as an LLC -- the rules are designed for corporations and not LLCs. The advice I usually give my clients is to dissolve the LLC and reincorporate as a corporation if you are interested in pursuing 501(c)(3) status.
Thank you for your question and best of luck!