Thor, I can think of two things I think would help you more than buying another splitter. First i would make a small boom with a winch to mount on your dump trailer, It would allow you to load trailer long logs on the trailer to dump and buck later. It will speed up the gathering of wood a lot as you would only have to make one or two cuts per tree instead of bucking everything into stove wood lengths, not to mention the boom would do all the heavy lifting. You can buck at home when you not under the end of the month time restraint. The second thing I would do is mount a second boom and winch on your splitter. I have a boom on my splitter and I use it for loading everything I dont feel like picking up by hand. I can use a set of log dogs to hook up a large round 20ft away from the splitter and load it without breaking a sweat, or my back. You can use the boom to hold up one half of a big split while you do the resplits on the other half of the round. This saves a ton of wrassling heavy wood and speeds things up a bunch without working harder.
I use my 6x10 homemade dump trailer to get logs in 10ft lengths, I have bucked before loading exactly one tree in my trailer in the last 3 or 4 years. I dump my logs close to my wood shed and buck when I dont have anything else to do. I pull my splitter up to my pile of rounds and use my boom to load the logs. Sometimes i back my trailer up under the splitter and let the splitter just push the splits back onto the trailer to be back under the wood shed and stacked, and sometimes I just let the splits pile up and use the tractor to scoop the wood and haul to the shed. I do very little manual lifting of my wood, and when I do it usually only after the wood has been reduced to splits that will fit in my stove.