Partial power on 12V

It might help if you clarify what the problem is.

Other than to power the charger (aka: converter), the 110v AC is irrelevant to the 12v DC side. Shore power is 110v AC, so no surprise that 12v loads such as slides or water pump work with or without shore power.

If all the 12v circuits are working fine, what's the issue? I'm guessing something is wrong when you connect the trailer connector (I understand it's a truck camper) but you don't say what the problem is.

what exactly is the new problem..  everything sounds like it is working but you said there is a new problem, with out you telling us what it is, it is hard to help you.  

• Shore power works fine only for 110 circuits.  - Yep, that's how they are supposed to work, that or a genset. 
• Slide and water pump work on 12V, with or without shore power connected. - Yep. Again, that's how they are supposed to work. Your 12V system works on batteries, not shore power. Shore power may charge the batteries, but all 12V items still run off those batteries. 
• Shutoff switch works properly, all 12V disconnects in the Off position. - Ok
• Batteries are charged, properly configured and connected. - OK
• All 12V fuses, and AC breakers [ohm'ed] good in fuse panel and on power converter. - OK, just remember, 12V and your AC run off 2 different power sources. 
• Problem exists whether 7-blade connector is connected to truck [2007.5 Dodge Ram 3500 6.7] or not. - What problem?
• New power converter installed, all 12V circuits functioned properly upon initialization and subsequently for several days prior to the new problem. All fuses on the converter [ohm'ed] good. - Again, what problem?

Hopefully you return to clarify but based on the information above, we can only assume a few things; Either you are confusing what runs on shore power vs what runs on batteries (12V), Or some of your 12V items are working and some are not. You didn't say that specifically but I'm guessing based on your last sentence.