Mixing Species?

I'd love to hear about people's experiences mixing species of parrots.

We currently have a lovely 2 year old blue head pionus female. She is sweet and mild, and friendly with other birds. She is fully flighted. We had two pionus girls, and they got along quite well; couldn't share a cage and didn't preen each other or anything like that, but followed each other room to room, bathed together, ate together etc. Engaged in flock behavior basically. And they never fought apart from our older girl chasing the younger away from her stuff.

Our other pionus girl, who we'd had for many years, was unintentionally brought outside (hiding in my husband's jacket) and flew away. We are absolutely devastated. Have spent weeks looking for her, posting all over, contacting vets etc, all to no avail. We have lots of hawks so I wonder if she was caught by a hawk right away.

My remaining blue head, Little Bit, is doing fine, but has become extremely clingy to me. She screams whenever I'm out of sight. The poor thing has never lived as an only bird. I know she might adjust with time, but we're also thinking, in a year or two when we've had enough time to mourn and we're done making a big move across the country, we might get a new bird friend for her.

The obvious would be to get another blue head. And likely that's what we'd do. But a part of me has always wanted an timneh grey. I'm just concerned that they're dissimilar enough in terms of species that they wouldn't provide much companionship, which would be a big reason to have another bird. I don't need them to be best friends, but I'd like them to be able to "flock up" and benefit one another psychologically that way. And certainly I would want them to be safe together when out and not intensely aggressive, especially as both would be fully flighted.

Anybody with luck developing healthy flock dynamics between old world and new world birds? Or should we just stick to the same species?