Recently bought and used the Camco swivel wand.
This is looks like a hose with a swivel at the end that when connected to a hose and stuck in to the toilet it spreads water at a very high speed and pressure.
My sensors had not been telling me that the black tank was empty since the day I first acquired my motor home, within ten minutes of having the swivel wand do its trick the sensors were down to one.
Highly recommended.
By the way the chemicals never worked.
My built-in BT flush hasn't worked in years, so I've been using a Cam-co straight wand with stationary spray-holes for quite a while. I had the same result as you. About a month ago, I found a straight want with the swivel end (similar to yours) and found it works even better! Glad it's worked for you, too!
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2013 Eagle 266RKS
2011 Ford F-150 w/3.5L Ecoboost & H.D. Tow Package