Ellie,
I used to direct a group that had for many years used Hilty assignments. When I became their director, I quickly weened them off of that into assignments that I thought were more reasonable and musical. However, they had 3 octaves and often only 10-11 ringers. Never as few as 6 or 8 though. When we only had 9 or 10, we basically did what you would do in any other assignment methodology, we used the "standard" assignments Hilty had used, then looked at the notes left unplayed by the open positions. After looking at the music, I would farm the remaining notes out on a case by case basis for what worked best in that piece of music. We also tried to give additional notes to ringers who were stronger and could handle the challenge of additional notes. Even if everyone was there, we found that in certain keys, there were still ringers who ended up having to 4ih to some extent when 3 of their 3-4 notes were quite busy.
You're probably asking because you're wanting to know what the assignments worked out to be. As always, it seems creating your own assignments as the director is the way to go based on the needs of your group and the piece of music. Ways I could see you accomplishing your goal:
1. Give the 6-8 ringers "standard" Hilty assignments and then divide the 3-5 remaining parts among them, either based on music/ability or perhaps related to the 'busyness" of the parts already spoken for. Perhaps one of the 6-8 parts isn't so busy and could take on a few more notes from the excess parts than the other ringers.
2. Give the 6-8 ringers 'standard" Hilty assignments and then divide the remaining parts among the ringers based on a standard assignment approach. For instance, if you have the F#5, C6, G6 part unassigned, perhaps it's possible to give the F#5 to the F#6 ringer, the C6 to the C7 ringer, and so on. Or maybe you could pair the reamining notes in a more standard fashion based on the music (e.g. A5 goes to the B5 ringer).
3. Re-devise a Hilty-style assignment system on your own. I rang with a group that used a modified Hilty assignment method in the bass, but chromatic (mostly) assignments in the treble. For instance, they assigned C3 and C#3 to Ringer 1, D3 to Ringer 2, Eb3 and E3 ro Ringer 3, F3 and F#3 to Ringer 4, and G3 to Ringer 5. Then, they would start assigning up from there starting with Ringer 1 again. Based on the key, the enharmonic notes would alternate from the ringers on either side. This did make it possible for less ringers to play more notes (C3-C5 is assigned to 6 ringers in "standard assignments" but they were able to assign all bass notes with only 5), but it also had challenges as well, as the assignments were in 6ths, which made stacked chords a challenge for one ringer to play. Thankfully, these ringers were good at sharing and helping each other out, so it worked. Anyway - devising your own Hilty-like assignment system might be possible. Maybe if you have 8 ringers, start with C4 and go up from there and see where it leads you, being careful to make sure one player doesn't get all the "accidentals" and another gets 4 natural notes.
4. Ask yourself is it really necessary to assign in this way for the project/music you're trying to accomplish, and would it be possible to use some other assignment possibilities that would be more useful and/or musical :-)
-Josh Fitzgerald