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Dorothy,
Have you had the soil in the new beds tested to see what deficiencies might exist? It's usually not a great idea to try to correct for problems without first knowing what you're starting with. Your local Cooperative Extension office probably offers soil testing services.

That said, compost is a good safe thing to add to most beds. This helps provide some nutrients and aids with soil texture, by reducing compaction and helping with moisture retention.

You do not need to soak the Iris bulbs.

These articles will help you.

https://www.gardeningknowhow.com/ornamental/bulbs/iris/planting-dutch-english-and-spanish-irises.htm
https://www.gardeningknowhow.com/ornamental/bulbs/iris/iris-plant-care.htm

This article will help understand this issue.

https://www.gardeningknowhow.com/ornamental/bulbs/iris/why-an-iris-changes-color.htm

Lack of flowers means it's time to lift and divide your plants!
How wonderful they are heirloom blooms.

Here are some links that will help you.
https://www.gardeningknowhow.com/ornamental/bulbs/daffodil/dividing-daffodil-bulbs.htm
https://www.gardeningknowhow.com/ornamental/bulbs/iris/divide-bearded-irises.htm

I would recommend potting the iris up for the move during this time of year. If the move is in the fall you can store the dormant rhizomes.

This article has more information.
https://www.gardeningknowhow.com/ornamental/bulbs/iris/storing-iris-rhizomes.htm

It is possible to move irises and lilies in the spring before they bloom, but they will probably not bloom this year because of the disruption. However, they will probably recover and bloom next year.

If it's possible to leave them until they bloom without destroying them when the fence is removed, that is the best option. If not, you might as well move them now.