Thanks to all for comments and feedback. I spent many hours using a 3 pt hitch mounted hydraulic splitter on a John Deere 2240 tractor in my younger days. 1,500 engine rpms and the ram speed was good (not too slow but not so fast as to make knotted oak splits exciting). The 2240 appears to have a pump rated at 9 gpm and 2,250 psi. The 4400 appears to be rated for 8.3 gpm and 2,500 psi, so sounds to me very similar. Is there an important detail or two I'm missing here that would make my 4400 work poorly compared to the 2240?
Since a 3 pt splitter is the only kind I have ever used, I hadn't considered a stand-alone unit with its own engine. However, keeping another engine serviced and running is a committment, and towing a stand-alone splitter on uneven/rough ground to where I need it isn't nearly as handy as one hanging on the 3 pt hitch. I don't mind running one from my tractor - I bought it to use and enjoy.
My main objective is to have a splitter that provides adequate splitting force and reasonable cycle times and doesn't cost a fortune to get my tractor set up to run. Again, if I'm missing something on the 4400's hydraulics, please let me know. Otherwise, I'll check with my local dealer on a Power Beyond kit as Dutch445 mentioned. I haven't googled what a Power Beyond kit is, but is it a pair of hydraulic outlets on the back of the tractor that either have pressure and flow full time OR have a separate SCV to control flow as needed?
Again, thanks to all for the input. Very thought provoking.