The three minimums you're seeing come from three different wrappers. Private funds sold under a securities exemption usually set minimums somewhere between $25,000 and $250,000, and institutional open-end debt funds often start at $1 million or more. The $2,500 product is almost certainly a registered or semi-registered vehicle, an interval fund or a non-traded credit fund, which can accept small checks because it's registered rather than exempt. Most of the private ones also require you to be an accredited investor, which is a defined status under securities rules, and the fund will ask you to document it. A securities attorney is the person to confirm your own status with.
On the gap between the 9% coupon and the 7.5% target, the line items to look for are the management fee, usually 1% to 1.5% a year, charged either on committed capital, invested capital, or net asset value. Which base they use matters more than the percentage. Then there's a performance fee or carried interest, often 10% to 20% of profits above a preferred return of maybe 6% to 8%. Then fund expenses, which cover the audit, the administrator, and the fund's legal work, often 15 to 50 basis points combined. Add loan losses and any cash the fund is holding uninvested and you've usually explained the difference.
When you compare published returns, check whether the number is gross or net of fees. Index figures for these funds are frequently quoted gross, and that's a full point or more above what a holder actually receives.