I'm wondering whether moving the bulbs to another spot in the yard might make a differece.
I'd certainly think it would make a difference. Can you tell if they are bearded irises or not? Are you familiar with what iris rhizomes look like? It it is irises, chances are they are too thick, and are not getting enough sun.

Can you get us a pic of them? I'm thinking they could also maybe be crocosmia as they have thin iris like foliage.

I would not not till them under....even if I knew what they were, but instead would try and dig them all out before tilling.

Below is what another member had to say about crocosmia bulbs left in the soil.
My mother-in-law had a front garden bed 10 by 10 foot that I dug all the soil out a foot deep and strained it through a half inch mesh hardware cloth to get those corms from the roots so I could replant the bed.

Sue

Here is a link that might be useful: Google images iris rhizomes

Almost any iris will be happier in sun, though there are exceptions: yellow flag iris being the most common exception (it will tolerate sun), but also roof iris. Crocosmia will like sun too.

That being said, the chances are you have tall bearded iris or, possibly siberian iris, since these are the ones most commonly planted.

Bearded iris foliage is tall, blue green, broadly sword shaped and arranged in fans. When you dig it up, there will be fat carrot like root/s (actually rhizomes) at a perfect 45 degree angle on the bottom of the foliage. It's very distinctive. When you dig and divide, you break off the old, mushy, dried out, etc. pieces of rhizomes and leave the younger, plumper, firmer ones.

To plant bearded iris, dig your hole, then make a mound in the middle of the hole whose top comes up to soil level. Place the rhizome on top of the mound and let the thinner roots that hang off the bottom of the rhizome lay over the top and sides of the mound. Hold the leaves upright with one hand and refill the hole with the other, covering the feeder roots, but leaving the top half of the rhizome exposed to the sun. Do not mulch over the rhizomes. That's an invitation to rot. This is the best time to divide and replant. If you put them into good soil and keep them watered, you'll almost certainly have blooms next year. Set each fan about eighteen inches apart from its brothers and sisters. You can cut the fan of leaves back by half if you want to. If you don't, the leaves may dry and die back for several inches anyway. Not to worry. this is normal for bearded iris.

Siberian iris foliage will be about 12 to 18 inches tall, medium to dark green, and only about 1 to 1 1/2 inches wide. It will grow in clumps with straight roots.

You'll do well to put your irises in a bed with full sun and plenty of organic material dug in. (Tall bearded iris really love manure.) I'm not a big fan of siberians, so cannot comment on their specific preferences.

If they've been hanging on to life under pines for a long time, they're probably good, old fashioned vigorous irises. I'd give them a new home and stand back.

Thank you. I'll give them another chance. I hate to kill flowers of any kind, but didn't want to plant something that would not survive transplanting.

Paula

Plus if they are overcrowded, irises could stop blooming - at least mine did, and when I transplanted a few clumps to other parts of the garden, they bloomed like crazy in their new spots, and thickened from mere clumps into small bushes. Meanwhile the original patch continues to have foliage but no flowers. Not sure if its the space being crowded or nutrients being depleted or what...