I have played in several weekend warrior classic/80s rock bands. In cover bands like this it's not really all that important to get the keys to sound exactly like the original records. Just take a look at Youtube videos of the band you mentioned that still tour and look at what synths they are using, none of them are using vintage synths.
A great option for weekend warrior classic rock type bands is the Casio XW-P1 because it has multiple synth engines that would work great.
The "solo synth" engine is a pretty good monophonic VA that makes great lead sounds. If you play songs like "Crystal Ball" from Styx you will easily find a patch for that classic lead sound.
It also has a great "draw bar organ" engine that sounds really nice and has an excellent Leslie simulation.
Then there is the "Hex Layer" engine which stacks up to 6 patches on top of each other. There are some great Piano and Pad/String sounds there as well as great general pads.
It is also very easy to setup your patches for easy switching during your set. You will also find a lot of the presets are geared towards cover bands. For example there is a patch called "Africa" that is is the sound from Toto's song Africa
The Casio goes for $500 so it is a real bargain for what it does, it is also very light weight and easy to transport.
Since you have a budget of up to $1500 and the Casio is only $500 I would also suggest getting a Korg Microstation for $399 and buying it from Sweetwater.com It has mini keys which I have found quite easy to adjust to, however you could also play it easily via MIDI from the XW-P1. It is a very good source of sounds for classic rock and has a very good synth engine as well. The cool thing about buying it from Sweetwater is they will also give you a SD card with an amazing virtual B3 program created by a guy named Daniel Fisher who works there. It sounds amazing.
The MicroStation also has a bunch of sounds from the Korg M1
including the great electric piano from the M1