Stuck truss rod nut.

First post. Awesome site and forum! Really appreciate info like this. So... I recently acquired a 460s-12 on CL for what I thought was a fairly good deal considering the condition. I checked it over carefully, even put a straight edge on the neck and found it had just a touch of negative relief. As it was missing a few strings and was way out of tune to the low side I figured it would straighten up with a new set. Otherwise the guitar sounds great, bridge has not been shaved and is not lifting. Some of the frets in the 3-5 range could use some attention but otherwise I was happy with the purchase. After I cleaned it up and put on a new set of strings I found that they indeed did straighten out the neck to almost dead flat, almost..... No prob, I'll just loosen the nut an eighth of a turn and we should be good... New CL lessen learned. Always check the nut! I've been checking out sites on how to fix it when I found this site. I hoping from the picture someone will chime in here. Best I can tell, the nut appears to be gunked to the rod. The hex wrench slot is in good shape so I know I'm getting a good purchase on the nut. I can move it maybe a 16th of a turn. It doesn't spring back when I turn it so I'm fairly sure the nut is actually moving on the rod, fairly.... It takes quite a bit of torque to make that happen. In theory the rod could be moving at the head stock end. I did make one of the neck adjusting tools hoping that if I remove the tension off the rod the nut would turn easier. No Joy. My next thought is to hit the nut with some penetrating cleaner. I have some SeaFoam DC-14 Deep cleaner that should free up any rust. I'm a very handy guy and my tool collection from Stewmac is only dwarfed by my collection of vintage oscilloscopes I use for messing with amps. So I'm not afraid to have at this. It's just an experience thing. How hard can I crank on that nut without breaking the rod? Though I printed your neck reset info, I really don't want to go that far yet. I am going to reach out to a local luthier to get an opinion, but the guitar is not worth spending much money on. Thoughts, words of wisdom, better cleaner suggestions?