Among the first hybrid chinas, as reported in The Old Rose Informant by Brent Dickerson, 2000, there are a few that may well corrispond to the renoncule shaped hybrid china The Shell rose, La Isla Bonita and Rose found in Samos.
“‘Du Luxembourg’ (Hardy, 1820 or before). We see many roses from Hardy proclaiming their place of origin, the Luxembourg Palace in Paris. This Hybrid China was described by Noisette as “Flowers pretty, very double, having the form of Ranunculus, petals in a spiral, of a charming violet color.” Prévost fils adds, “Ovary glabrous, short, oval-pyriform. Flower small, full, regular, purple red with edges brown-purple or deep violet.” Hardy was to release what were presumably improvements on this Ranunculus-shaped hybrid a few years later, a ‘Renoncule Violette’ in 1824, and a ‘Renoncule Brune’ by 1828 - both Hybrid Chinas again.”

Does anyone know the size of this rose?

I recently checked several references, and found that at the time Mary Lawrence published her book(1799), there were no Hybrid Chinas yet. She has the Shell Rose as a Centifolia, and is probably correct, as she seems to have been careful about her identifications. The found rose that tested as having Gallica and China can therefore not possibly be the Shell Rose.