So I saw a new TTi QL355T offered for less than half the list price, and could not resist.
Turns out the instrument is out of spec, i.e. its voltage deviates more than the specified 0.03% + 5 mV at higher voltages (where the summand becomes smaller in proportion). Its feet had been attached wrongly, and the front plate is askew.
I have returned it for a refund. I'm not sure whether this is typical for TTi's QC?
Thanks for any opinions.