Prequalification letters for ETA deals with post LOI equity raise

I am currently working through a lender brokerage prequalification process on an ETA style acquisition where the broker is requiring a prequalification letter, and I wanted to sanity check lender fit. In the ETA model, my understanding has always been that lenders prequalify based on deal economics and operator profile, with equity formally raised post LOI and subject to diligence. I am comfortable outlining an equity plan and investor profile, but committed capital would come later. I am finding that the broker’s preferred lender path is underwriting prequalification closer to final approval and only counting currently committed equity (personal cash), which feels less search friendly and likely to result in a decline. Would appreciate any advice on navigating this and recommendations for SBA lenders who are comfortable issuing conditional prequalification or comfort letters in ETA or search style deals, assuming equity is raised post LOI. My goal would be to have a credible fallback to say, your preferred lender is not a fit, but I was able to get prequalified elsewhere.