I had the same situation. I bought a soft core drum baler, OMC brand, but same as a Gehl 1310 or 1710. It works great for me when I run out of time, or storage or out of help for square bales. BUT mine is a very big heavy high HP OMC baler.
I think the advice you got here for baler size and brands/models is good. I did a lot of homework before I bought it and found the baler model I wanted at a consignment farm auction.
But, your idea of a round baler to handle the excess has worked for me.