Here is an idea for Psalm 44

A. 1 We have heard with our ears, O God, our fathers have told us,
what work thou didst in their days, in the times of old.

B. 2 How thou didst drive out the heathen with thy hand, and plantedst them; how thou didst afflict the people, and cast them out.

C. 3 For they got not the land in possession by their own SWORD, neither did their own arm SAVE them:

D. but THY right hand, and THINE arm, and the light of THY countenance,
because thou hadst a favour unto them.

E. 4 Thou art my King, O God: command deliverances for Jacob.

D’. 5 Through THEE will we push down our enemies: through THY name will we tread them under that rise up against us.

C’.  6 For I will not trust in my BOW, neither shall my SWORD SAVE me.

B’. 7 But thou hast saved us from our enemies, and hast put them to shame that hated us.

A’.  8 In God we boast all the day long, and praise thy name for ever.
Selah.

There seems to be a clear turning point at v4 – the focus for the first three verse is on “the times of old”, but after this it is about God’s help to the psalmist at the time of writing. v1 links to Exodus 12 v 26, where the children of Israel were commanded to tell their children about the meaning of the passover, and what God had done for them, then v8 talks about the psalmist telling about God’s works in their lives.