We ran into this exact situation with a client a while back. The VPN route is tempting, but LinkedIn is surprisingly good at fingerprinting beyond just IP - browser, timezone, device, session patterns, they look at all of it. A Texas VPN won't mask most of that.
What actually works is separating access from execution. Your team in India does everything except the actual sending - research, copy, sequences, the full prep. Then you use an outreach tool where the client installs a browser extension on her end, and the campaign runs through her local browser. LinkedIn sees her real location, her real device, nothing looks suspicious.
The other option is she handles a short daily task herself, like approving and sending a batch you've prepped. Some agencies build this into their workflow just to keep liability off the table.
Logging in directly from India is the one thing I'd actively avoid. It's not about getting caught immediately - it's that one flag can trigger a review. Sales Navigator accounts that get restricted mid-campaign are a nightmare to recover, and your client relationship takes the hit, not LinkedIn.