The first part (about the speed) is clear enough.

However, what does the second part mean? Does it mean that the Strain becomes both Strain and Recovery (and that the Strain is unusually delayed until Recovery is gone)? That's how I'm reading it but it seems very harsh. For example, would a normal attack with a Gladius be Speed 7, Recovery 3, Strain (delayed) 3 and a Mighty Swing with a Gladius be Speed 8, Recovery 6, Strain (delayed) 3?

Yep!

Messy spell, but considering the alpha strike damage, more than justified.

It definitely has the potential for a large alpha strike but still really harsh. A Mighty Smite gives you an effective Strain of 9 for purposes of 0ing it out (but only 3 if you wanted to cast through it). Then again, a Mighty Smite Smite would be Speed weapon+4, +pIn to hit, and damage weapon+(Mi)+d6+d4+(Ch)+5 (very likely to cause massive damage) but Recovery 6 and (delayed) Strain 3 (and uses a once per scene ability).

what I usually see is that the spell goes off and someone then uses a Fate point to wipe the recovery or strain.