If I understand your question right, you are thinking about getting the DC input for the inverter from the converter panel?
When you convert the 1000W AC (and I would guess the surge wattage is much higher) to amp draw on the DC side, its way over 30amps. Your inverter manual should have the info. The issue is going to be the wiring from the battery to the panel is too small. Its probably something like 10 gauge now. For a 1000W inverter, it depends on the length of the run (again, check the inverter manual) but you will need something like 2 gauge or 1/0.
I wouldn't mess with the converter wiring. Any way to put the inverter in a front storage cabinet accessable from the inside? You would probably have to drill 2 holes in the floor and then use a strain relief and some silicone to seal them up, but the inverter should have properly sized cables and be as close to the battery as possible, but in a dry location.
A little more work, but would give you a permanent or semi-permanet setup that should be reliable - and since you have it, you might find other times its handy. We got our first inverter to power 110V awning lights on our popup and used it a lot.
2005 F-150 FX4
2013 Rockwood Roo 23 IKSS