Those older deck mount converters are not all that bad. When I renovated my '71 I chose to keep the old PD-808. Mine also has the 12v distribution integral to the converter. There are probably 3 or more fuses behind the hinged front plate.
I'd suggest to keep the converter you have and use it for the trailer power and auxiliary battery charger. Basically, don't do anything with it. Get your new fancy battery charger and connect that to the existing battery when needed or hardwire it in. I'd leave it portable so you can use it somewhere else. If you get enough solar power going, you won't need a charger. Mine hasn't been run in over a year.
As to an inverter, listen to the wise ones on here that have used their inverters. You WANT a pure sine inverter. The additional cost between MSW and PSW will evaporate the first time a cheap inverter fries a laptop or phone charger. Your other entertainment gear and anything with a selector switch will not get along with the cheap MSW either. Beyond that, cheap inverters fail within a year or so, it's your money.
If you have any questions about your '71 and need some help, post it up in the Forum or send me a PM. I like me some vintage travel trailer.
EDit: I see there was some speculation about the existing converter. The input draw at 120V is 3 amps. The output is 20 amps (might be different and you should at least measure voltage across the battery terminals when you operate it) so you know what you have. If you have solar and a standalone charger, the output is moot since the 20 amps will serve your cabin loads well. If you get in a situation where you want to charge the battery fast, you can connect all three chargers to the battery-solar, existing, and the new standalone.
BTW, I have some analog gauges for my electrical (and a Victron monitor). The installation of the gauges is easy, connect 12V gauges to the 12V wiring in the easiest spot, same with 120V if you are going to monitor that. An amperage gauge is best with a shunt since that will enable you to monitor the draw to/from the battery and not inline at some odd place. Turnigy meters are well respected around here but there are cheaper solutions.
I have pictures of some of this in my restoration thread in my signature line, The Cowboy/Hilton.
