You can slow down weapon speed as well using an additional effect. Here are the magic effects that you will be interested in:
1) VoiceSlowTimeEffect (magnitude is a fraction of 1.0, so for instance, 0.5 = time moves at half speed)
2) AlchDamageSpeed (magnitude is a percentage value, so 30.0 would lower speed by 30% to a total of 70%)
3) PerkDualFlurryWeaponSpeed (magnitude is a fraction of 1.0, so 0.5 = half speed)
4) AlchFortifyCarryWeight (set magnitude to 0.01 -- this is required for speed changes to be registered by the game)
My suggestion is to duplicate all of these effects and make your own versions of them. You will have to change all of their magic effect types from "fire and forget" to "constant effect" so that you can use them as an ability, then you will have to make a new spell of the type "ability" that uses that effect and sets its magnitude to whatever you'd like. Then you could set up a perk that applies them all which you can add/remove from the player at will.
I have used a setup just like this for a similar slow time effect. The way I did it was to first create a new perk. Then add 4 new perk entries, ticking the "ability" radio button, and adding one of your four new spells to each entry. You will have to select a higher priority in the perk entries for the speed spells, so that they get applied before the carryweight change--which forces the game to recognize the speed changes.
Edit: you may want to keep in mind that if you want this effect to only happen while the player is at low health/stamina, it may take a bit of more complicated scripting to achieve that effect. It isn't very straightforward to detect when the player is low on health, unfortunately.