I don't like the recipe much.
First of all, paella is a one pan dish, normally. That is, all ingredients are cooked in the same pan (paella) and in sequence. This means that all the flavors are stacked one on top of the other.
Second, if you are going to use saffron, the most expensive spice in the world, hold down on any other spices. In particular, most recipes I've seen, use paprika powder explicitly forbidding the use of 'de la Vera (smoked)' paprika powder.
Third, if you are going to use saffron, at least treat it with delicacy. Put a pinch of saffron in a cup of warm chicken broth before you start cooking. This way, the saffron will release it's color and flavor slowly. When you must add the broth, first add the saffron broth, then the rest.
Fourth, this recipe has way too much ingredients: Chicken, Chorizo, Lobster, Shrimp, Squid, Mussels, Clams in the protein department. Honey, Saffron, Garlic, Pepper and Parsley in the flavor department.
Fifth, Spanish paella (Arborio Bomba) rice has a thick grain that resists cooking that long.
Having said all that, and to answer your question. If you are using saffron, don't use the smoked chicken as you'll not be able to taste where your money went. If not, and if you insist on using this recipe, go ahead. Paella really accepts all you want to put into it (but do look for a simpler recipe).
I am wondering if it will be ok to cook them till they are cooked and then drain them, clean them and put them in some fresh water with some garlic and butter to cook again...
Yes that should be fine, just make sure you discard any shells that have not opened by the end of cooking as those are dead ones.
Here's a nice recipe for moules marinières, mussels cooked with butter, white wine, shallots, cream and herbs which also explains how to de-beard them.
Best Answer
With regards to the grit, if they aren't farmed mussels (which generally are fairly clean) you may want to give them a soak for a while. This will give them the chance to expel any further sand/grid they may contain. There are varying theories of whether to use tap water, salt water, sea water or various other concoctions. And admittedly there are those who say any form of soaking will do all sorts of harm to the flavour. But if the alternative is disappointing gritty mussels, why not give it a try.
And as always, ask your fishmonger for advice. They will know the origin of the product, and whether or not you need to take extra steps in preparing them.
As for discarding opened mussels, don't just discard them when they seem open on arrival. If the shell is not cracked, give them a light tap (on the counter or with a knife) and see whether or not they will close in response. If they close in response, they are fine. If they don't close or tell you to stop it, then discard them.
And if two thirds of the batch really are dead ... I personally would not necessarily trust the other third to be in great shape.