The signal timeout for this call is indeed hard-coded to 300ms, see here and here.
"context deadline exceeded" errors typically indicate errors caused by a timeout that happened, so my best guess is yes that timeout is causing the SignalWithStartWorkflow call to fail.
I would open an issue for this to make it configurable via dynamicconfig, or to at least move it up to 400ms so it for example matches the timeout set for parentClosePolicy.