Okay, I think I did it:
I ended up implementing the trick above because other solutions seemed less intuitive. A template-row-level button wouldn’t work because that button wouldn’t know which client you’re adding the row for (unless you assigned that client onto a Platform record, which would’ve been a spaghetti solution)
It copies data from the template into C+T rows, but if you’re fine with lookup formulas you can clean those copying up.
I know it may be a lot to take in for someone who’s not so experienced with Coda. Unfortunately, loss of outer CurrentValue is a known problem and there’s no beginner-friendly workaround for that. The most bulletproof and logical solution is the one I implemented; in some cases it may be avoided but not yours.