I Googled "Carpet lilies" and it seems that most of the lilies sold as such are low growing Asiatic Lilies. I know that these lilies are very robust and quick to increase. They are also tolerant of a wide range of different soils and conditions
'Stargazer' and 'Casa Blanca' belong to the Oriental lilies and these can actually be a bit temperamental. Some can grow them very well, but often they don't increase much and they also are well known to dwindle over the years. You probably already know this, but they also require an acid soil. For this reason it's actually often recommended to grow them in pots, so if this works for you, then I think you should continue
If you like the fragrance and size of Oriental lilies, but feel that you would like a more vigorous lily it could be well worth to look at the OT(Oriental Trumpet) lilies as they usually are much easier to grow in the garden. They are also sometimes sold as Orienpets. They may take a year or two to settle in, but after that, they usually are very strong growing and they can grow in both acid and alkaline soils. Apologize if you already grow a bunch of these, but I thought it was well worth mentioning. And just as you know, OTs are my favourite lilies, so I'm very biased
. 'Silk Road' for instance is a great, garden tested OT lily that is widely available, grows very quickly and blooms for a very long time as well.