I have played keys in a disco 70's band. Brass and strings are easy for modern synths, pianos too. But proper Hammonds and Rhodes take a bit more effort. There are a number of soft synths that do the one thing. The German company NI are good at this, they have really good Hammond soft syth.
My keyboard was OKish at Rhodes and Hammond, the brass/string/clav/piano and other sounds were good. Also my keyboard was good for live playing were I can change sounds/key splits real easy. This was good for the 70s disco as I would often use brass and piano or something and flick between the two mid song. So all I took to the gig was the one keyboard which would easily cover all the sounds.
But I would guess for your application a fast computer running a collection of soft synths would be good. It would depend on how realistic you need the Rhodes to be. It takes so much time and effort to audition synths, then find one at a good price etc. The computer is much easier.
As for the keyboard player coming then going, well this seems to be the norm with musos that have not signed a binding contract. I have had enough of pamering to musos in an attempt to get them to do the job, but they usually drop by the wayside. My next outfit needs to have some form of contract written up but that will also have to include some regular income etc. Ohh it's all getting too complex already!