Even though it's the wrong season, I would encourage you to plant them if they are special to you. That being said, I'm an unconventional garden in that I don't always go by the book. I grew up poor and was taught to garden by my mother and grandmother who were very old fashioned. If you had something beautiful that you wish you could grow again, you did what you could to help it get a start. The idea of "throwing them out and buying some new ones at the right time of year" wasn't a thought that even occurred to them.
So, if I were you, I'd let them bloom and enjoy the heck out of them and then, I'd read up on planting tulips---figure out the best spot in your garden for them, prep the soil as recommended, etc. and then plant them this spring. Alternatively, there might be some things out there in Google-land about summering the bulbs over in the dark, but I'm not sure if that would make them want to sprout in the fall.
My mother and I have done what I'm recommending with Easter Lilies that the church was throwing out. They were also "forced" bulbs, but when taken care of, they did establish themselves.
All that said, just this weekend I've been doing what I'm recommending to you (I'm quite a bit further south from you, in Northeast Kansas where spring is well underway). A local homestead has been sold and much of the lawn & gardens are going under the plow to make more corn & bean fields. The lady who lived there up until this past year spent a good 40 years developing her bulb, iris, perennial gardens. Her family took what they wanted, but the majority was left and offered to anyone who wanted something before the dozers came in. So, in that case it's---even though it's the wrong time of year, do you go ahead and dig whatever you can/want and hope for the best, or just let it be lost? My sister and I spent about 3 hours digging on Friday (we barely made a dent in what was there) and on Saturday I planted all of the perennial plants that I dug up and tons of daffodils of all kinds here in my own gardens. I still have 2 large 50 lb. dog food bags of Bearded Iris rhizomes to plant.
Apologies for the wall of text, I didn't mean to go on for so long! Best of luck with your future garden endeavors!
TL/DR If you love growing beautiful things, why not plant them? If you enjoy gardening, there's nothing to loose.