I would put the bulbs (in clumps, not singles) in the empty spaces between the perennials. The perennials shouldn't be cut down if they are still green, and I don't see how that would matter in regard to bulb planting. It's not unusual that the perennials didn't bloom this year - they were busy growing roots and establishing themselves. Next year should be good, but the year after next, you should get an awesome show from them.

The annuals are your choice, whether or not you want those spaces for the bulbs. Maybe leave some for the seeds and remove some to make more room for bulbs? But what about next year's annuals? Will you want spaces for those?

Ideally, I like to put spring-blooming bulbs in the holes when I'm planting perennials - a loose ring around the edges - to get the most out of my digging efforts and the space in the garden. That's rarely practical, though, with bulbs being bought in fall and perennials/annuals usually in spring, but ideal when it works out, like with last-chance clearance plants, or with plants that you bought in spring but never planted yet, cuttings you struck during the summer, etc...

I position my bulbs just behind the perennials so the ugly dying bulb leaves are hidden behind the incoming perennials in the summer. Cutting off the bulb leaves too early can drain the bulbs of energy for next season.