Raising an Africa focused fund

Greetings,
I, along a group of professionals are working on raising a micro sized fund ($1 million as a start) and we are targeting a specific group of diaspora community. We have been doing the research/surveys and have found out that there is a great demand within that community. However, our investors are going to be American citizens/residents with average incomes and our targeted investments are SMEs that are privately held in a specific African country (among the fastest growing economies in the world).

Before we begin working with lawyers, we are doing our own research on how to structure this fund. We know that PEs, HFs, and VCs are out of the picture as they are only for accredited investors by law. Open-ended Mutual Funds are the most realistic for our purpose that we have come across but we are concerned about the liquidity regulation as Mutual Funds must be able to redeem shares at the end of the day should investors demand it. As our money will be tied up in private companies, it won't be easy to remain liquid. A close-ended fund on the other hand will require us to list on an exchange which is way beyond our league. I am wondering if there are other types of investment funds that we are not aware of and would work with our goal. Your suggestions are kindly appreciated.

Note: we are not necessarily planning to open an office or get ourselves salaries in case you are wondering how we are going to manage the costs with such a tiny fund.