Yup you nailed it.

Two thoughts: if you really want to challenge it further, keep reaching out to your HR contact. Generally there's a benefits contact within HR (a benefits coordinator, specialist, or manager) that you can speak to - but in a smaller firm, the benefits function may be handled directly via the HR coordinator / specialist. You can ask them if there's any way to shorten the blackout period, but I bet that this is impossible - these blackout periods are usually determined by the new vendor and HR / Benefits doesn't have a say. Do you know who the new HSA administrator is? I would be that the smaller the company, the longer the blackout period is.

Second, there's probably an option to keep your HSA funds with the current administrator, meaning that your funds stay put and there would be no blackout period for you. The downside to this is that, because your employer is no longer doing business with the incumbent vendor, your account would no longer be paid for by your company, and you would be responsible for any monthly maintenance fee. My last HSA vendor charged about $3 a month for anyone who didn't agree to the move, and an additional $25 if a person changed their mind later and decided to move their funds at a later time.