I've found a partial record for this man online, though I've no idea of its provenance.
This gives:
10 Dec 1915 - Volunteered
10 May 1916 - Called up for Service
3 Jul 1917 - Transferred from 1st Wessex Bde RFA to B Battery 227 Bde RFA in Trowbridge
21 Jan 1920 - Transferred to Army Reserve
If correct, and it looks valid, this suggests that our man stayed with a TF unit even after transferring to the Reguar Army.
Looking again at the longlongtrail explanation, this states that a man's Service Number would only change when he was actually transferred outside of his Corps. So presumably our man retained his TF number until it was updated in c.March,1917. He would then have changed to a Regular Service Number when he was moved to 227 Brigade, RFA.
That all looks to work.
As I understand it, 217 Brigade, RFA was the 1/3rd Wessex Brigade, RFA (TF) component. While 227 Brigade, RFA was the 2/3rd Wessex Brigade, RFA (TF) component. Continued references to the 3rd Wessex Brigade, RFA (TF) would therefore actually refer to the 3/3rd Wessex Brigade, RFA (TF) component.