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If the deep is full, add the super. Then obtain extra equip. I would never be without extra equip. You will always get caught short if you do.

Generally in this area a deep and a medium are devoted to brood. The bees will store some honey in these. Another medium with honey over that is usually what you want for the bees to have over winter. A strong hive may have more mediums, but most of mine have not been so strong that I could not reduce to a deep and 2-3 mediums for the Winter. I usually take off the "honey" medium in early August when I am doing mite treatments, as much to reduce the "fumigation" area as for any other reason, and then place it back on the hive after the treatment is completed. If stores are low in other parts of the hive and there is not much of a flow, I am prepared to feed sugar water during the treatment periods. I am also prepared to feed after the flow is over if the bees need more food to build up and if they need to put up sugar water "honey" for the Winter.

You should be doing your mite counts and have a treatment plan in place. I am leaning toward early August treatments, where needed, with Apilife Var. This will give time for the treatment to take effect and then to have enough brood cycles for the bees to build for Winter.

I would not put on an excluder. At this point, you are trying to build the bee population from a new nuc so that it will successfully over winter, and not make a honey crop to take for yourself. The excluder will keep the queen out of the comb that you would want her to be laying in. When you have enough room for brood and winter stores, you can consider putting an excluder on in the future for honey frames. I don't generally use excluders and put them in only for specific reasons and for a short a time as necessary.

Another hive body would be better. Then you could move a couple of frames up from the lower box and replace them with empties. That will give them space to work in the bottom while they are expanding into the second deep.

Avoid the excluder, give the queen room to work. As they fill the frames and the queen reduces egg laying in the fall/winter, they will fill in what they can with honey stores.