That $2k cash restriction sounds like HealthEquity, which is who my employer uses. I set up a separate HSA at Fidelity and quarterly I initiate a transfer from Fidelity- I found that doing it from the Fidelity side was FAR easier than working with HealthEquity to initiate the transfer. Unfortunately I don't think there's a way to set up recurring transfers so I just have a recurring calendar reminder to do it quarterly.
It takes a couple weeks to process (I suspect they actually mail a paper form to HealthEquity, who then mails a check back to them, sadly). On the Fidelity side, from the Transfers menu you want to choose the option to "transfer an account to Fidelity" and then later in the process when it asks you what you want to transfer I choose cash only and I transfer all but ~$50 in the account. If it asks you if you want to do a "partial transfer" say yes, otherwise they may consider it a request to close the original and move everything to Fidelity.
Lastly, and something I have forgotten more than once - after the transaction has settled and the funds are in Fidelity, they're only in the cash/settlement fund, so you want to be sure to go back in and actually buy your index funds with it!