Having gone through transcripts of the Parish registers for Mildenhall and Barton Mills recently I thought you might be interested in the following.I didn't find any addtional Barton Mills baptisms over than what you already have but there were a number in Mildenhall, icluding what I believe is the James you are after.The spellings are as per the transcript.
Thomas AGGIS & Mary Ann - Betsy AGGESbpd. 7 Aug 1785 - James AGGISbpd. 26 Jun 1791 - Joseph AGGISbpd. 14 Dec 1794 - Thomas AGGISSbpd. 1 Jan 1797 - Mary Ann AGGUSbpd. 22 Jul 1798, bur. 1 Dec 1800
William AGGIS & Sarah - John AGGISbpd. 8 Feb 1789 - Sarah AGISSbpd. 1 Apr 1792 - William AGGISbpd. 3 May 1795
Betsy Aggus had an illegitamate child in Mildenhall: - Edward Aggusbpd 11 Jan 1809