The Trollius ledebouri I grew from seed via winter sowing 4+ years ago appears happy where it's planted in part sun at the northwest corner of my garden. The soil is sandy loam; the plants get no supplemental water. I mulch heavily over corrugated cardboard so my plants don't compete with weeds or encroaching brambles.

According to Larry Hodgson's book 'Perennials for Every Purpose:' "Cool and wet. Those are the conditions you need if you want to succeed with globeflowers." Included under that heading is Trollius x cultorum although 'Alabaster' is not mentioned specifically by cultivar name.

Mulch may explain why I've had no issues with self-seeding. I do enjoy the cheerful blooms early in the season, more particularly because they attract pollinators and don't appear to be bothered by pests.

For me, Trollius x cultorum (mine is 'Cheddar'...I think) has been very slow. Even in a shady area that is almost always moist it has been weak. The foliage looks terrible after blooming, which is why it is planted amongst other things, used almost like a spring ephemeral.

It's a bit of a toss-up. Your T. cultorum would probably prefer the damp/shady area to its current home if it is that dry. BUT I'm not sure if it could stand up to more rampant neighbors. I wouldn't chance it myself, but in your situation it may prove more vigorous.

I know it's not what you asked about but...Trollius chinensis ('Golden Queen') is extremely stout and could easily contend with your wild plants. For years I stayed away from Globeflowers because the tag and book blurbs of their requirements always made them seem fussy. This guy isn't at all. It's even braved a root-y area that dries out easily. It seeds around a bit, which I am more than fine with.
CMK