The problem is that there is no single reliable source for artillery equipment changes. Probably the only way to do it is to look at unit War diaries, and hope they made a note of changes. However, converting to 4.5-in would probably need a period to allow for individual training and a work-up exercise. Since medium arty was seldom under command below corps level Joslen is no help.
At the outbreak of war 7 Med had a bty each of 60-pr and 6-in. They seem to have kept them at least until Feb 41. They're difficult to track because in 1941 they spent various perods with their two btys in differnet places. 7 Med's two btys were 25/26 and 27/28, but RHQ sometimes had a bty from another med regt under command.
It's not clear what they were equipped with in Greece. Neither Horner's 'The Gunners' (Australian) nor Farndale's 'The Years of Defeat' give any information. However, the other medium regt in Greece, 64, went there equipped with 4.5-in. This regt seems to have started re-equipping in very early Mar 1941 and arrived in Greece on 20 Mar. 7 Med arrived there 2 weeks later. During Mar/Apr they were part of BTE, which could mean re-equipping.
When 64 Med arrived back in Egypt having lost their guns in Greece they were re-equipped with 6-in, indicating that there weren't any 4.5-in guns available. In Syria in Jul 41 7 Med appears to have had 6-in in at least one bty.
From 7/10/41 until 19/8/42 RHQ and 27/28 Bty were BTE while 25/26 Bty was 8 Army. The regt joined 8 Army at the second date.
I don't have any detail about the period from late 41. This one is definitely in the jigsaw category.