How long have you actually had the mantis (sorry if I missed, just skimmed the thread). I've had mine for maybe 4 or 5 months now I think and she has progressively become more and more interactive and confident being out of her cave while I'm around. I'm unsure if this is helpful as I don't know your setup, but you could try angling the pipe so that the entrances are visible. Mine spends maybe 60% of the day with its head sitcking out looking around from inside her pipe/cave, 30% hidden somewhere and 10% actively running around the tank exploring, moving rocks etc.
For the first two months I owned her, that ratio was more like 20% sticking head out, 80% completely hidden and very occasionally I'd see her outside of her cave.
Behaviour also changes signficiantly around moulting.
I'd echo getting a faster fish, damsels and six line wrasses are both likely to fare pretty well. I also think adding some weedy (fast growing, very hardy) corals such as green star polyps, Xenia and maybe some zoas would be a great idea. Getting much deeper into corals than that can be very expensive both in time and money, and I wouldn't recommend that for you right now.
FWIW they do seem to have personalities. My shrimp lives with a Molly I acclimated from fresh water (great fish, constantly swimming around eating algae) and has absolutely no interest in it, the snails or any hermit crabs around the tank. However, I add glass shrimp to supplement her diet and when they go in she becomes a murderous maniac until they're all gone (except for one particular shrimp that's been in there for months that she doesn't ever bother??).
Adding some macro algae could also be a great idea, add some more colour and movement to the tank easily, and it will also help suck up nitrates and keep the water clean.
Best of luck!
I've had her for coming on 6 weeks now, so it's really encouraging to know that yours spent more of her time out and about and being visible further down the timeline than I've reached yet. My first few weeks sound very much like yours. It's definitely possible as others have said that my water quality issues are messing with her unpredictable ways. Funnily enough as I've been replying to posts this morning for the last 30 minutes or so, she's been in and out of the burrow entrances patrolling the tank and swimming up the walls of the tank which is lovely to see.
I do have all three burrow entrances front facing so that I get the pleasure of her company whenever she's poking her head out.
Also great to hear your take on the damsel and/or six line wrasse idea. I definitely feel like that's the way I want to go once I get my water quality under control. Same with corals - the advice I'm getting consistently from every source is go with cheap, easy soft corals like xenia, green star, zoas and toadstools. seems eminently sensible, although again, when my water quality is stable - no other creature deserves to go through the nitrogen cycle I've put Oatmeal through. I'll definitely also experiment with some cleanup crew at some point too.
I've also heard the macro algae recommendation before too and I think it's a good idea which I'm going to look into.
Thanks again for all your advice - this post really helped me