Last fall I planted tulips (White Emperor, I think) and muscari. They flowered beautifully. But I'm afraid I only planted them 2 or 3 inches deep.

I want them both to perennialize, and I'm worried the tulips are too shallowly-planted to survive the winter. So I had an idea I want to run by y'all:

In the fall, once the bulbs have lost their foliage, I can add a layer of soil, compost, and/or mulch on top of them, to correct their planting depth and help them survive the winter.

Do you think I should try it? If so, what should I add: soil, compost, mulch, or some combination thereof? If not, what should I do instead?

I live in Central Texas, zone 8b. The soil is heavy clay that can be pretty soggy in the winter. I've amended it where I planted the bulbs, but it's still pretty moist.

Some thoughts on your zone planting, article from https://www.colorblends.com/re...

Recommendations for Southern Planting
Most bulbs do well through Zone 7 in the South. In Zones 7-10, where soil temperatures do not cool down sufficiently in winter, and spring weather is often very warm, many bulbs perform poorly unless they are pre-chilled – i.e., refrigerated for 8-10 weeks prior to planting. Here is a rundown of the bulbs we carry and what special treatment they require, if any, to perform well in the Deep South.
Tulips
Tulips need to be pre-chilled to bloom well in Zones 7b-10. They should be placed in the refrigerator (NOT freezer) in October for 8-10 weeks, then planted in December when the weather cools down. Without chilling, plants will be stunted and the flowers will open down in the leaves. Once you take the bulbs out of the fridge, plant them right away. Don't let the bulbs sit in the sun while you are digging.
In the Deep South (and much of California), tulips should be considered an annual and new ones planted each year. We have lots of southern customers who are comfortable with planting every year but it is really a budget decision. The tulips on our Southern Recommended page seem to handle the cooling process and southern heat pretty well. Some species tulips can return for several years – namely Bakeri Liliac Wonder, Clusiana Tubergen's Gem, Linifolia and Tinka.

Grape Hyacinth (Muscari)
We recommend that grape hyacinths be pre-chilled. They may come back for a year or two in Zone 8.