For these 3 pots:
Glazed or Plastic Pots Planted With Tulips,Hyacinthoides and Allium
Glazed or Plastic Pots Planted With Lilies , Allium, Tulips
Clematis w/ tulips, allium, in glazed pots
The bulbs all need a chill period, so they need to be somewhere cold, though it doesn't have to be below freezing. I don't know how long the cold period needs to be, though, so you might need to research that. I also don't know how cold you get in the winter and for how long and what your tolerance is for losing pots or plants. To minimize loss, you don't want them to be really wet and freeze since the expansion of freezing soil may damage your pots (both plastic and glazed ceramic), and you can't let them get super dry since that will damage the plants. If they get too cold that may also damage the plants, so typical rule of thumb is to use plants that are hardy to 2 zones colder than yours for exposed pots. I have a feeling that both the shed and the screen porch will be ambient outside temps and will only have the advantage of letting you control moisture, and so I'd choose to place these on the steps under your bulkhead. They will stay a bit warmer, but still get good chill, and you can monitor moisture levels. In early spring after danger of severe cold has passed, move to the screen porch so that they get good light, or an outside spot where they don't get too much moisture, like under an overhang. Burial might work for you (depending on duration and extent of really cold temperatures) but I don't think I'd want to chance the pots, and those would have to be mighty large holes. You'd need to insulate over the soil surface with mulch or weighted down sheets of builders insulation (ugly!) since exposed soil freezes much more deeply than covered soil. Regardless, cover all the outdoor, bulkhead, and cellar pots with hardware cloth covers since mice and voles might find your bulbs and perhaps other plants to be good food sources.

The only other of your plants that I've overwintered are Dahlias and tuberous begonias. Last winter which was quite mild, the Dahlias stayed in pots in my unheated and sunny entryway. Both the pots and the Dahlias survived total benign neglect no water or attention all winter. I was surprised to see that they had survived, but I might suggest that a cool dryish indoor location like your cellar might do better. Someone wiser & more experienced than I should advise you about when to start watering and bringing them into the light.

My tuberous begonias go into a setting like your plant room (my east-facing cool kitchen windows.) They die back and I just tuck them under the bench holding other tender perennials until spring. I water them just enough so that they don't get overly dry, perhaps once a month a little bit. They start growing on their own when the time is right and I bring them up into the light then. Putting them outside on above freezing days might help them be less leggy - I am going to try that this spring with one of my pots.

Fine Gardening has this to say about care and overwintering of Rex begonias:

Rex Begonia
Conditions: Considered perennials in tropical and semitropical climates, Rex begonias are frost tender and typically grown as annuals or houseplants in North America. They thrive in organic, sharp-draining soil and in shade with lots of humidity.
Care: Watering "on demand" (or when the soil is dry to the touch) is a great way to keep Rex begonias happy. Avoid soggy conditions, but do not allow plants to wilt. Give Rex begonias a diluted dose of organic, soluble food every four to six weeks during the growing season. Begonias do not grow or use fertilizer efficiently below 58F.
Overwintering: Rex begonias make excellent houseplants and can easily be overwintered indoors. To supply plants with adequate humidity, place containers on a tray of gravel, where runoff water may collect, evaporate, and raise the air-moisture level. Avoid placing plants near drafts.

Here is a link that might be useful: Fine Gardening article on Rex begonias