All right, let me be brutally honest. What is it you think a tube amp is going to give you (or do you just want to try one to see what all the "fuss" is about?). Did you get the Advents with a tube amp in mind? I ask because there are better old speakers to mate with a tube amp than the Advent.
The Advent isn’t (by current standards) particularly transparent, and is on the warm side of neutral (imo). A tube amp of the old-fashioned, classic type (Dynaco, for one) won’t help matters (inexpensive tube amps---the RM-10 being the rare exception---tend to error likewise. The Advent was designed to be powered by a solid state amp, with a low output impedance.).
Maybe a modest tube pre-amp (with your budget, look at the Schitt Saga +) and a decent medium-powered solid state power amp (used Parasound A23?) would be the way to go. But I say that as one ignorant about current integrateds. Separate power amps are almost all superior to the amp section of integrateds (imo), especially at the $1,000 level. Too bad the NAD 3020 is underpowered!