I would not cross-connect a deep-cycle with a normal starting battery
they charge/discharge at different rates and its not likely to end well for one of the battery's
and no I would not recommend bypassing the charging brick and running 12v thats idiotic to say the least
what you can do is get a decent dc-dc boost converter and set it to the needed voltage (just make sure its a quality one and not some cheap garbage )
finally if you wanna charge via SOLAR a MPPT is the way to go
RVs and campervans all connect starter batteries with deep cycle batteries though? I know most of them make use of Inverters and Voltage sensitive split relays, which is practically what I'm looking to install in my van.