I'm sorry, I did not see your post earlier, or I would have answered.
The Auburn University plum varieties you list all came out of a long term breeding program that was conducted by Joe Norton. Auburn's program stated way back in the 1950's. Mr. Norton was quite successful, as his releases included Crimson, Purple, Homeside, AU-Producer, AU-Roadside, AU-Cherry, AU-Amber, AU-Rosa and AU-Rubrum. Of the ones you ask about:
AU-Amber is a medium sized plum with reddish-purple skin and yellowish flesh that is so-so firm, but not firm enough for long distance shipping, but firm enough for local use. The tree is resistant to bacterial spot and canker, but is susceptible to black knot. Unfortunately the tree is self-infertile, therefore needs a pollinator of the Japanese hybrid type. However, it is a good variety for the humid Southeastern States. Requires 600-700 winter chilling hours.
AU Homeside is a large red to orange skinned fruit (2-1/2, inches) with a yellow/white flesh. The taste of Homeside is VERY GOOD. The flesh is not firm enough for shipping, but OK for home growers. The tree is very vigorous and grows to be a large spreading tree. Resistant (or tolerant) to black knot, canker, bacterial fruit spot and leaf spot. NOTE: This variety requires at least 700 hours of winter chilling.
AU Roadside: is a medium sized tree, producing dark red skinned, and dark red flesh fruit with a good taste. Roadside's dark red flesh is much firmer than the above two varieties, and would make an excellent variety for the fresh market. It has resistance (or tolerance) to black knot, bacterial canker, fruit spot and leaf scald, with some amount (?) of resistance to brown rot. The excellent fruit quality was inherited from both of it parents. Fortunately Roadside is a self fertile tree and flowers heavily, and set a heavy crop. A good choice.
AU Rosa: Is a medium sized tree producing large red skinned fruit with yellow flesh. The plum has a good taste, and firm flesh. Just moderately resistant to bacterial spot and canker, but tolerant to plum leaf scald and brown rot. NOTE: AU Rosa requires about 750 winter chilling hours. A good variety for the humid Southeast. Self infertile, needs a pollinator, blooms about the same time as Santa Rosa.
AU Producer: is a large, very productive, vigorous upright-spreading tree, with dark green leaves. The mid-season fruit is medium large (1-1/2 inches) with dark purplish red skin and dark red flesh. Producer's dark red flesh is of EXCELLENT quality, as well as appearance, and it is very firm, making it a good candidate for shipping and long storage. In your area should mature about June 25th. It has high resistance to bacterial fruit spot, canker and leaf spot, with a tolerance to black knot. Producer was developed for the south because of the high disease pressures. It is one of the main commercial plum varieties in the Southeastern United States. The chilling requirement is about 750 ours.
This would be an excellent choice, I highly recommend this tree.
You did not ask, but the variety AU Rubrum is a self fruitful, heavy bloomer, sets heavy crops of quality scarlet red skinned, red flesh fruit that is VERY LARGE (2-1/2 inches). Good tasting for fresh eating. One of the larger sized plums for your area.
Byrongold: was produce by J.M Thompson from an open pollinated lot of seedlings. It is a large yellow plum with good tasting firm deep yellow flesh. The fruit is well adapted for the fresh market, ripening about the last week of June in your area. Resistant to bacterial and fungal diseases which are common in the southeastern United States. The flowers of Byron gold are aromatic providing an extra blessing. Sometimes heavy thinning is necessary as the fruit set can be more than adequate. The fruit may be picked while still retaining a green trace on the yellow skin, if storage is wanted.
Hope this answers your needs. Happy New Years to you and your family. - Millet