If you put them in storage now they are likely to die and survivors won't be in good condition to flower next year.
You can try gently transplanting them from the barrel to the ground, where they can go dormant when they are ready. Cut off any maturing fruits, just below the fruit. Water them until they start to go dormant. After flowering they need to grow for a couple of months to get ready for flowering next year.
Next year, try planting them in pots sunk in soil in the barrel. Then you simply transplant the pot, with minimal disturbance to the tulips.
No. Unsightly as they get, leave them alone until the leaves are completely died down. Then lift the bulbs and store them - let them air dry for a day or two first, of course. As long as the leaves are green, they are gathering the strength that will make them bloom next year. If you were to pull them now, you could bet they wouldn't blossom next year.
literally pulling them might separate the leaves from the base and that will not be good for forming a new bulb for next year. :-o
so if you have to remove them and can't tip the planter and take the whole clump, dig gently from an angle farther away and see if you can scoup the whole thing out (supporting the stems with one hand and the bulb clump/roots with the other).
then move the whole clump someplace else that it can be left alone until the foliage dies back naturally. keep moist if needed until it starts yellowing and then stop watering. you can pull the foliage off or trim it once it yellows, but if you have no fungus problems or other problems leave it alone until it dries completely.
after that it's normal fall bulb care for them (depending upon your area, goals, etc. this can be different :) ).
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