Re: warm chorus
that chorusy purple rain rhythm guitar part was played by Wendy Melvoin. Videos of that era show her using a rickenbacker into a roland jazz chorus amp. HAving owned a jazz chorus i can definitely attest to the lushness of its chorus sound.
However, prince has always famously been a user of boss pedals. Even to the point of him eschewing the super expensive and amazing bradshaw rack system he had built, to go back to his old skool boss inline setup.
So, unless you want lug around a large and heavy JC120, see if you can get your hands on a boss ce-2. They are getting expensive these days, but not too bad. They do sound lush. If not, then it is pretty easy to mod the ce-3 stereo chorus so it sounds the same. The other one worth looking at is the voodoo labs chorus (sounds like a boss ce-1). All three of these pedals are discontinued but they are all pretty nice. Its funny, i just realized i hate using chorus, but i've owned all of these over the years!
You can probably get pretty close to any or all of these old skool analog choruses with something more recent tho. There are plenty of boutique makers out there.
Re: knobs. More knobs means a more complex circuit. Take that as you will, but in my experience, more is rarely more when it comes to any guitar circuit.