This is a property of all transformers, so I’m afraid you’re likely to be stuck with it. The magnitude of the impedance might be somewhat less with a higher-rated transformer, but other factors, like phase shift, could easily spoil everything.
Not really. If you do filter (excessively), you’ll end up not measuring the power in the harmonics, which will introduce a deliberate error. It ought not to be a large error, because the power in the harmonics should, if your loads obey the rules, be small. But you don’t know that they do and whether it is or it isn’t negligible.