I love the texture in Rip City FX's chum. Their booth was across from our SWSCA booth at a Halloween and Haunted Attraction Industry convention in Portland. (West Coast Haunters Convention) and I got to play with their chum a bit. I did not ask/hear about it being mouth safe or edible, so I can't comment there.
A lot of shows use actual meat (bbq chicken, pork, beef, etc) and mouth safe blood. The only issue there (beyond possibility of vegetarian actors) is the mint-flavored edible bloods usually create a... interesting flavor profile when mixed with BBQ.
You just need to make sure the meat (and surface you apply it to) is kept sanitary and things are stored at safe temperatures. Making sure you have a single person who owns that responsibility is key.
For vegetarian alternatives I would use gelatin with additives for texture. Mixing in different powders could lower the materials transparency. Think safe edible things like cocoa, non dairy creamer powder or liquid, drink mix powders, etc. Just keep in mind that the color of your additive will impact the color of your gelatin, and its flavor.
For texture you could add pretty much anything. Stringy foods like thin noodles or long/thin sprouts (possibly with tops removed) could help simulate meaty textures.
There are some leafy vegetables like "frisee" that have an interesting texture. It may be possible to soak them in a saturated food coloring mixture, dry them, then add them to gelatin.
You could also use a shredder to make a durable vegetable into stringy muscle fibers.
Another idea would be to brush hot gelatin onto a silicone cooking sheet in thin strips to create muscle fibers. I think this option has a lot of potential.
Those painted strips could be pigmented to look rather solid, and then mixed with gelatin that is a bit more translucent to create a good muscle look. Playing with varying translucencies could help add dimension and contrast.
I would suggest freezing your gelatin fibers before introducing them to a hot base gelatin, and letting that base cool as much as possible before mixing. You may even be able to brush it on.
In addition to insuring your edible gore is kept on ice, make sure your actors have no food allergies. Best to avoid anything containing dairy or proteins that can easily spoil, and go gluten/nut free if possible.
Sounds like a fun project and a messy day or two in the kitchen!
If you paint it yourself you'll lear more. You may not love the result as much, but you'll get closer to doing paint jobs you will love. Also, you can always re-paint it until you get the look you are after!
For holding up under water, alcohol based makeups will be the most durable. One option would be to use alcohol makeups for the body/face and then do the area around the eyes with cream, grease, or silicone based makeups. Using a sealing spray may also help things hold up a bit more on the face. Though touchups will likely br needed.