What kind of tree is that?

Asking about the tree to know if it is one that is more surface rooted and would compete with the surface rooted azaleas and rhododendrons...

But aside from that - "There's a lot of limestone here". Do you happen to know the approximate ph of your soil - rhododendrons and azaleas need an acidic soil to thrive and that lower ph isn't usually supported by limestone.

Since the tree and the limestone will probably cause problems with a rhododendron and azalea bed, I recommend a raised bed. It will circumvent both problems. I would recommend placing a layer of gravel under the bed to facilitate aeration of the tree roots.

Raised Beds: Rhododendrons and azaleas need three things, acidic soil, drainage and drainage. If the soil is poorly drained or alkaline, a raised bed may be the best option. Rhododendrons and azaleas have shallow roots, so the raised bed only needs to be 6 to 12 inches above grade. Create it by creating a mound or berm, or a raised planting bed using a retaining curb such as logs, timbers or rocks. It is best if the base is a material with good drainage like gravel. Then at least 6 of 8 inches of good acidic, well-drained soil above that. If you use a lot of peat moss or compost remember, the peat moss and compost will decompose over time to 1/2 the original depth, so make the bed proportionately deeper. [Sketch courtesy of Harold Greer]

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When preparing new raised beds in soil that is not acidic, the pH may be lowered by adding flowers of sulfur (powdered sulfur). Amounts of powdered sulfur needed to lower the pH of a silt loam soil to a 6-inch depth are given in the table above. A target pH of 5.5 is ideal for most rhododendrons and azaleas. Sandy soils would require less and clay soils would require more. Elemental sulfur is converted to sulfuric acid by soil bacteria. Therefore, in order for sulfur to work the following must be satisfied:

Sulfur must be mixed with the soil to provide contact. (Around established rhododendrons and azaleas, do not disturb the shallow roots. Sprinkle the sulfur under the mulch and then replace the mulch.)

The soil must be moist
The soil must be aerated (bacteria need oxygen).
The soil must be warm for rapid bacterial growth.
Time is required for the reaction to go to completion.

Good Luck!

Here is a link that might be useful: How to care for rhododendrons and azaleas.