Can multiple castings of Glyph of Warding be used to activate multiple “Smite” spells on the same triggering attack?

Suppose a character has cast multiple Glyph of Warding spells, each with a different "Smite" spell (such as Searing Smite and Thunderous Smite). Assume the character somehow has access to all these spells and the necessary material resources. Each glyph is set to trigger at the character’s next successful melee weapon attack.

When the glyph is triggered, the stored spell is cast.

Each "Smite" spell requires concentration, and has a target of "self", so the character specifies their self as the target when they create the glyphs. Each "Smite" spell also has an on-hit effect that can occur during the spell’s duration, triggered by a successful melee weapon attack.

For example, the character has one glyph set to activate Searing Smite, and another glyph set to activate Wrathful Smite.

Searing Smite:

The next time you hit a creature with a melee weapon attack during the spell’s duration… the attack deals an extra 1d6 fire damage to the target…

Wrathful Smite:

The next time you hit with a melee weapon attack during this spell’s duration, your attack deals an extra 1d6 psychic damage…

Upon the character’s next successful weapon attack, all the glyphs activate. Since the duration of each "Smite" spell begins on this weapon attack, can the character use this same attack to activate the on-hit effects of each spell? (In the above example, that would mean adding +1d6 fire and +1d6 psychic damage to the weapon’s damage roll.)

Or does only one spell effect occur, because they all require concentration and their durations would overlap?

Or do none of the on-hit effects occur, because the spell’s duration began after the weapon attack?