Yes, unfortunately there is no other way.
Someone could theoretically "share" their Strike account as an omnibus, but that would probably fall under the definition of a "money transmitter," and you'd need a license to do that.
Discussion
But you guys are money transmitters, why not just forward the funds along to a third party wallet?
To get a money transmitter license, you must follow those pesky regulations - KYC, AML, etc.
But maybe I didn't understand your original question.
What would be the benefit of having this setup? You can connect BTCPayServer directly to a third-party wallet (and use Breez for LN liquidity).
Strike provides FIAT settlements, so merchants are hedged against BTC price volatility and can easily withdraw money to their bank accounts.