I found an FAQ for the return to play.
https://media.nhl.com/site/vasset/public/attachments/2020/07/14036/FAQ - Return To Play - FINAL - 07.13.20.pdf
'Traveling Party' answers my question about chiro and massage therapy. Amusingly, each team must bring at least one content creator/social media individual.
There's really not a lot of wiggle room then for who to bring:
31 players
3 coaches
2 trainers
1 equipment manager
1 massage therapist
1 chiro
1 PR/communications
1 social media
1 'club compliance officer'
The league might let a team combine social media with PR/communications as is common in minor pro. Club compliance sounds like a specialized role here. The person is required to have prior compliance experience.
So if we're min/max'ing, 31+11 = 42 (keeping PR and social media split)
That's 9 spots flexible. The 52nd spot would be for team security.
TB has 5 coaches (Coop, Richards, Halps, Newsy, Jean), so we're at 44.
Let's say two execs (JBB, Roest, Murray, Darche, etc.) putting it at 46.
Bringing a strength and conditioning coach sounds useful. 47.
Maybe someone tech-savvy from stats, video, or pro scouting to make sure that backend collection stuff is running correctly during games? 48.
Equipment managers might be able to band together in Toronto, which would take the pressure off to bring more. While they're not changing cities, they are changing rinks, and they've got to get in and out at certain times because these rinks will be busy all day at the start. I really think teams will take at least two though because they know their guys. So 49.
That's only 2 spots left for more execs, pro scouts, equipment, or whoever. They don't have to be used, but teams can't bring everyone, even with 52 spots.