I have the transcription of parish registers for Rowington 1612-1812 I think, if you'd like any lookups let me know.
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About 'my' Averns so far I have a marriage + a few baptisms int he 1680's + 1690's now there are a lot of Averns around at this time + unfortunately I cannot connect them up yet.
The family is old in Rowington + I think it must all be connected as Avern is an uncommon name + Rowington was + still is a small place.
In a book call 'Anne to Hroca' about rowington, it mentions an old building called the Malt house, and then says the AVERN family inhabited this house from 1546-1853, I would love to connect this but cannot so far.
We may work out a connection sometime, anyway look forward to hearing from you