Barlow 4.5.1803 at Joseph Johnson's / 27.7.1803 again / 1.6.1805 Barlow at Philips
The GD website has coded these entries to Joel Barlow DNB 1754-1812. In the editorial notes to his person record it says that the diary (i.e. Godwin's diary) suggests that he returned to America via London. The DNB says he had returned to America by August 1805 so the timing is possible, but it could certainly have been another person called Barlow. Since most guests at Johnson's and Phillips' were authors I can only find John Barlow "teacher of languages geography and the globes" whose poem on the Loss of the 'Earl of Abergavenny' was printed at Weymouth in 1805 (near to where the ship sank). There was also Peter Barlow DNB 1776-1862 mathematician but he had no books published till 1811
Joel Barlow was proposed as an honorary member of the Socy for Const Info 9.3.1792 by John Horne Tooke 2nded William Sharpe