Clients want to pay in crypto, but I'm stuck between "not your keys" and needing fiat for expenses - how do you bridge this gap?

Started getting requests from international clients who want to pay in BTC/stablecoins to avoid wire fees and currency conversion nightmares. Great in theory, but here's my problem -I still need to pay rent, suppliers, employees, taxes - all in fiat. So I need to: 1) Accept crypto payment 2) Convert to fiat 3) Move to business bank account 4) Actually use it

Right now my process is clunky as hell. Client sends USDT. I move it to an exchange (Kraken/Coinbase). Sell for USD. Withdraw to bank (2-5 days + fees). Finally use the money.
Total time: 3-7 days. Total fees: ~3-4% by the time everything's done.
I looked into services that supposedly handle both crypto and traditional banking in one place with instant on/off ramps, but then I'm back to the fundamental question: if I'm giving someone else custody of my crypto, am I really using crypto the right way?

The whole point of Bitcoin is "be your own bank" and "not your keys, not your coins." I get it. I believe in it. But practically speaking, if I'm running a business that operates in the fiat world, I NEED that bridge. And every time I manually move crypto → exchange → bank, I'm wasting time, paying multiple fees, creating tax reporting nightmares, risking price volatility during the process.
How are Bitcoin-accepting businesses actually handling this? Do you keep everything in cold storage and manually convert only when needed? Or do you use custodial services for operational funds? The purity test - am I betraying Bitcoin principles by using a service that holds keys for me, even if it makes business operations smoother? Stablecoins as the middle ground? I'm thinking USDC/USDT for business operations, BTC for holding. Does this make sense or am I overthinking it? Tax implications - every crypto-to-fiat conversion is a taxable event. How are you managing this without going insane?

I want to embrace crypto payments. Clients love it, fees are lower, settlement is faster. But the last-mile problem of actually USING that money in the real economy is still painful. Is there a better way, or is this just the reality until more vendors accept crypto directly? Curious how other business owners in this space are navigating this.