A 10EE doesn't have a clutch, but it isn't a geared lathe either, motor's belt goes directly to the spindle, and I'm assuming you're using a VFD to control spindle speed. So probably similar to spinning up the mass going up to many lathe clutches. Depends a bit on whether your converted machine still has the reduction gear. If your 10EE's VFD doesn't support single phase input, you could replace it with one that does. Generally that requires oversizing the VFD. That's a very practical approach if you don't need 3 phase for anything else in the shop.
On RPC's, it is possible to add idler motors. (A common approach in some shops is to start a smaller machine first, then start the bigger machine, the smaller machine acts like another idler motor). The limitation on this is how many amps your RPC is wired for, and how many amps the contactors will handle.
A 25HP idler is going to have a really hefty inrush when the RPC is started. My 20HP idler peaks at about 200amps on the single phase when started. For your situation, most I'd be looking for is a 15 HP idler based system because I oversize everything. 10HP rated is almost certainly fine, the reality is you are running 7.5HP in a 10EE not for the peak HP, but to get decent torque at very low RPM (sub 60Hz), and the VFD provides soft start. Larger idler motor is just more idle current, that cost can add up.