I obtained seeds for an annual form: Asperula orientale.
But on doing more research found that there are many more
species some of which may be good alpine or rock garden candidates. Does anyone grow these?

yes!
They are lovely
I have two
Woodruff (Asperula suberosa)
this year

and
Woodruff (Asperula gussonii)
and somewhere I have a current picture, but not handy in the moment...

Thanks---I will need to check the hardiness of those two.
That one is very pretty.

Well, I have seen a reference that says A. gussonii is "fully hardy", whatever that means. They are both alpines and as such are able to withstand brutal winters. I'd say it's worth a try

Yes, I will need to see if they are offered here.

Asperula odorata/sweet woodruff is hardy here in zone 4a. It's a wonderful ground cover. Very interesting and pretty foliage all season, white starry flowers in the spring. I like the pink gussonii too, Dirt...will see if it would survive here.

here is gussonii just waking up this year

We have Sweet Woodruff in our Botanical Garden and it does fine. Good to zone 3. The suberosa looks to be good only to zone 5.

Thanks......I will look for seeds and/or plants.