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Though these products can certainly offer protection, there is danger of excess heat and moisture building up; even on cold days.
Wait and see, and I suspect your plants will recover.

https://www.gardeningknowhow.com/plant-problems/environmental/plant-covering-materials.htm

Echium can act a biennials and may not bloom the first year they are planted.
This article has care information.

https://www.gardeningknowhow.com/ornamental/flowers/tower-of-jewels/echium-tower-of-jewels-info.htm

The ones that are dead will not come back. They are biennials. This means that the first year is spent growing the leaves, while the second will set a flower spike, thus completing its life cycle.

There is good news, though. These flowers drop seeds like crazy. You will have more come up but they will take 2 years to complete their cycle again.

Here is an article for more information: https://www.gardeningknowhow.com/ornamental/flowers/tower-of-jewels/echium-tower-of-jewels-info.htm

What is your climate zone? These are only suited for USDA zones 9-11. Some varieties are short lived anyway. They will reseed themselves, but I'm not sure what variety that you have. This link will help you to find your climate zone: https://www.gardeningknowhow.com/planting-zones/usda-planting-zone-map.htm

This is best grown in a final container size of between 4 and 8 gallons, ideally about 10L will do.

They are self fertile so will always produce viable seed. Once the flowers have faded, you can either leave the (brown) flower spike where it is or cut it down and shake the seeds (one in each ex-flower, the size of a pin head) around the garden. The seeds seem to remain viable for many years and might germinate anytime from the same year they flowered to 15 years hence. If you like them, you'll need to get to recognize the seedlings so as not to weed them but to leave them.

The mulch should not be an issue. If they are growing, do not disturb!