Tulips often only have a couple of years worth of blooms, so not worth moving them. In general I would just hope for the best for the ones you have planted, and add more in places that won’t be too wet. Unless there is actually standing water in the bed for a day after a rain I bet your bulbs will be fine.

You want to wait for them to die completely back. You can dead head the flowers but leave the leaves to send energy back to bulb for the winter.
I don't cut my spring bulb plants back until mid-June. They are planted in a bed with other summer flowers (Glads, Daylilies) so the dying back plant gets hidden pretty well. Most of mine are previous years' Easter flowers. After they have graced my table, I dig a hole in the beds, toss the bulbs in and hope for the best. If they come back great, if not, oh well.

This is my first year planting fall bulbs (tulips, hyacinth, etc). They did amazing this spring and I am now hooked on bulbs! The problem is that they are in areas that get a lot of moisture from rain. I've read they don't like wet bulbs in the summer and that I should dig them up. Should I do this and replant them in the fall? Or should I just assume they'll die, and plant new ones in the fall?