I doubt a 944 is anymore expensive to run on a track day as your typical hot hatch. A mate of mine used to track his Pug 306 GTi6 and he would go through a set of pads and discs every track day - not to mention the number of pairs of front tyres he would shred. It cost him a fortune and he no longer tracks his car (he's currently got a Civic Type R which has never seen the track). Because the 944 has very substantial brakes as standard they will stand upto years worth of track days. I used to change his disks and pads for him. I doubt the front disks are a quarter of the width of an early 944 Turbo/S2 disk and the later 944 turbo'scars have even thicker front disks. It's the same principle for othe components such as wheel bearings, transmission, gearbox, engine. I even managed to return relatively reasonable fuel consumption at my last track day considering!!
I'm struggling to think of a more suitable car than a 924/944/968 as a track day car. They are relatively cheap to buy, not too bad on running costs, are robust enough to drive to the track, run on the track and drive home again at the end of the day (unlike your Elises that have an appetite for head gaskets I believe), and can provide as much RWD fun as you want.