CAPwTDIs said:
Upon refilling, it has lost ~1/4-1/2 inch a day, but I cannot identify any leakage.
Never go back to this shop. They obviously think you're an idiot who will believe any diagnosis they give you.
Local shop checked it over and said they do not see any leaks but suggested it may be losing fluid in the engine. Only solution would be to rebuild.
You could have something as simple as a slow leak that only happens at operating temps, and while driving, so that you're not finding spots in your garage. Or it could be a blown headgasket or cracked block/head, but that seems unlikely.
There are a few ways to tell if coolant is leaking into the engine: Pull the dipstick and look for greyish sludge, could mean a blown headgasket. Look under the oil cap, again for presence of sludge. Cloud of white smoke, which could also mean a blown headgasket. Pressure test the cooling system.
Car has new transmission.
Maybe someone screwed something up during the transmission change.
Could this become a driveability/safety issue if not addressed ASAP
You might get stranded on a busy interstate late at night because the engine overheat due to low/no coolant, so this would be a safery/driveability issue.
If you live in a cold area, a leaking headgasket could cause starting issues.
should I continue to monitor and supplement fluids as needed?
I wouldn't keep putting a band-aid on the problem. Either take it to another competent shop or find a guru in the regional thread appropriate for your location. Continued driving, even if you're vigileant about topping up the coolant, could lead to further damage to the engine.