There is an apparently hidden synonym here of 'Florida Rose'; but a rose known as the 'Florida Cottager' was a different rose: Gainesville Nurseries catalog of 1906, p. 6, lists 'Florida Cottager' ("Well known and common throughout the South; a constant bloomer; color bright red") separately from 'Louis Philippe' ("A strong grower and another favorite; the color is a dark, rich velvet, with lighter shadings to center").

Apparently Mr. Jones was responsible for breeding all of the roses mentioned in the following (with Dingee & Conard as their introducer):

“Long ago it was known that different varieties would hybridize or mix with each other, that is that the pollen would mix producing seed, that might under some circumstances produce varieties in which some qualities of both the parents, so to speak, might be blended or represented together in the new variety, and knowing this it occurred to a skillful hybridizer in this country, one who had made it almost a life business, that if he could combine the best qualities of the choicest varieties now in existence, he might secure something far better and more valuable, than any of the parents, and this is just what he has tried to do. He selected some of the best types of Roses for parents, and after years of patient study succeeded in hybridizing them under conditions that precluded the possibility of other mixture, and from this seed these new varieties have been produced. It is an exceedingly interesting illustration of what skillful hybridization can do, and no doubt the Roses will be watched with much interest. The names of these Pedigree Roses are, ‘Henry M. Stanley’, ‘Pearl Rivers’, ‘Mrs. Jesse Fremont’, ‘Maud Little’, and ‘Golden Gate’. The Stanley was named in honor of the great African explorer, and was raised from ‘Madame Lambert’ and ‘Comtesse Riza du Parc’; it is clear pink in color, and very beautiful. The ‘Pearl Rivers’ is raised from those two noble Roses, ‘Devoniensis’ and ‘Madame de Watteville’, color ivory white. ‘Mrs. Jesse Fremont’ is a seedling from ‘Duchess de Brabant’. ’Maud Little' is raised from ‘Pierre St. Cyr’ and ‘Duchess de Brabant’, and has a particularly lustrous bloom. ‘Golden Gate’ comes from ‘Safrano’ and ‘Cornelia Cook’, and is one of the most distinct and unique Roses recently introduced; altogether they are a charming addition to our list of New Roses, and will no doubt be largely sought after. It is certainly time that more attention was given in this country to the production of new and valuable varieties of Roses and other flowers and fruits, and though it is a matter requiring careful study and patient industry, it is believed that it will pay well if followed up with good judgment and skill, in fact a good many people are now doing quite a handsome business in introducing new varieties of various kinds, and there is undoubtedly room for a great many more.” [Success with Flowers, vol. 1, 1890, pp. 6–7]

The New Orleans connection is supported by the names 'Pearl Rivers', journalist of the New Orleans Picayune, and poet, and 'Maud Little', probably the daughter or wife of New Orleans florist R.N. Little (himself responsible for 'Winnie Davis'). Meantime, the magazine Success with Flowers was from Dingee & Conard, so they certainly speak authoritatively in the above comments.

I find zero references to 'Niles Cochet' before its offering by the California Nursery Company of Niles, California, in 1911. References to 'Niles Cochet' as if dating back to 1906 appear to result from confusion with 'Helen Gould', which was referred to for a time as the 'Red Cochet' or 'Red Maman Cochet'. For instance, a ‘Red Maman Cochet’ is listed in a 1906 advertisement—with ‘Pink Maman Cochet’, ‘Yellow Maman Cochet’, and ‘White Maman Cochet’ and many other roses—as a premium available to subscribers to The Epitomist, with the roses all supplied by Good & Reese; but at that time it was a synonym for ‘Helen Gould’, as specifically stated in the Good & Reese catalog for 1906 (p. 20). Good and Reese indeed seem to acknowledge this when, more than two decades later, they call 'Niles Cochet' "the TRUE Red Cochet" (my emphasis) in their 1929 catalog.