T I am not sure of any other Aikido method that removes the Uke/Tori relationship in this manner.
There is something very similar yet different to the Shodokan \ Tomiki Randori in Korindo Aikido. the main difference: Korindo Randori is not competitive, hence - we do not use full force, but do use variations disallowed in Shodokan \ Tomiki. Similarly to your style, reversals are allowed and the Uke and Tori roles switch continuously.
I once played with friend who learns Shodokan \ Tomiki Aikido (he returned to Israel from Japan for a visit) and it was a lot of fun. Though I did have a feeling of him trying to force techniques by strength and speed while I think he found it weird I was using techniques and variations discouraged in his Randori.