An American Christmas Harp does list Wade as the translator of the Hither ye faithful translation. I'm not sure why it's so listed, but I'm sure the editor/compiler is on the fasola discussion group, so if you ask there you might find out.
The 1834 version in Lloyd's has 3 verses. 1 is Hither, ye faithful. 2 is Jesus, for such wondrous condescension (Chocolate Pi's 2. without the O, but the O is needed to make it scan). 3 is Shout his almighty name (Sacred Harp 2) This version does have difficulty with scanning, you have to come in on the down beat the way the Oakeley version does on after verse one, instead of the upbeat with the 1st pitch repeated.
I did find Foundation in a hymnal from 1897, published in Harrisburg, PA by a group called the United Evangelical Church. In the composer spot on the page it was listed as American Spiritual.