Connecting to iPhone / Zwift and Garmin 945 at the same time causes problems

My configuration is to use my new Vector 3 (dual) pedals as the power and cadence source in Zwift on iPhone (Bluetooth), but to also connect my Garmin watch (945) to display cycling dynamics and record data.  However at least half the time I do this, there are severe problems.  The power numbers can vary significantly, there are drop-outs, and Zwift shows as connected but no power numbers.  If I turn off my Garmin 945 and restart everything with just the phone connection, it seems reliable.  Is this not a supported scenario?  Is there something I can do to make it reliable?  When it does work it is very nice.