The structure itself is not the problem. The problem is what the C buyer's conventional lender decides to do when it sees a same-day or near-same-day chain of title.
Conventional lenders vary significantly on this. Some regional banks will fund the B-to-C leg without issue if there is a reasonable spread between the A-B and B-C closing timestamps, meaningful value documentation in the file, and a title company that handles both legs cleanly and separately. Others see the back-to-back chain, flag a potential flip, and either kill the file or demand a seasoning period that makes transactional funding irrelevant. The assumption doing the most work in your Q3 timeline is that the C buyer's bank has not yet reviewed the full chain of title. Once underwriting pulls it, their internal policy takes over, and you cannot negotiate your way around that.
The specific risk you have not mentioned: the C buyer's lender may have no written policy on this at all, which means the decision lands with an individual underwriter. That is a worse position than a lender with a documented policy that is restrictive, because at least you know early. Get the C buyer to ask her loan officer directly whether the bank has underwritten a double-close transaction before, and ask for the answer in writing or via email. If the loan officer cannot answer the question, escalate to underwriting before you go further.
Transactional funding is still the right tool for the A-B leg if the double close structure survives scrutiny. The capital structure on your side is not what kills this deal. What kills it is the C lender's title seasoning stance, and that answer exists in writing somewhere inside that regional bank's guidelines.
What is the spread you are showing between the A-B and B-C closings, and has your title company confirmed they have closed this structure successfully with a conventional end buyer at this specific county recorder's office?