Different species matabolize drugs differently. There's a pain med that's marketed for dogs and for horses... the 50-lb dog dose is the exact same dose as a 1000-lb horse dose. Differences in metabolism. A small to medium sized dog gets 10x or more the dose of thyroid meds as a human would get. A 40-lb dog gets the same dose of Pepcid as your average (150+lb) human. Etc.
The exotic animal formulary lists metacam at 1-2mg/kg, with 0.5mg/kg used in some cases. With dogs you don't want to go above 0.1mg/kg for long-term use. IIRC, I've seen metcam used most frequently at about 0.5mg/kg in rabbits and rodents, which would work out to 0.1-0.2cc of the 1.5mg/mL formulation for your average chinchilla. Some people think that metacam is needed twice a day in rabbits because they metabolize it faster than dogs and cats do.
There is no hard truth. There aren't any studies in rabbits or rodents of this drug (to my knowledge), so people use what seems to work without causing problems. This is the problem with working with exotics. In dogs, side effects of this drug include stomach and intestinal bleeding, kidney and liver problems. I wouldn't expect it to make a critter sleepy.
I don't know why they dispensed 0.5mg/mL instead of 1.5mg/mL - I usually only send home 0.5mg/mL if the volume given will be less than 0.5cc, and this is in dogs - but that's for ease of administration, not because the amount of drug given will change.
Looks to me like your vet isn't wrong. Maybe they felt the chin needs a bit higher dose. Maybe the lower dose has not seemed to work for your vet in the past. There's a dozen different maybes, but when you've got wide ranges of doses available, I think it's reasonable to choose a middle-of-the-road dose (somewhere between 0.5mg/kg and 2mg/kg). Watch for diarrhea and changes in poop color.
And BTW, the tip of a standard 1cc syringe will fit inside the tip of the idiot metacam dispensing syringe. So no cutting up of bottle is needed (that idiot tip also comes out if you grab it with pliers and twist/pull, so again, no cutting up needed
). Pull metacam into the metacam syringe, then pull your dose out of that into your final syringe. It's a pain in the butt, but it's doable, and easier (IMO) than sticking the syringe into the bottle.