As I'm sure you already know that this is a very tough question to answer, if even possible. I get this question ALL the time when installing solar. There are some reasonably constant variables, but most are hard to predict on-going.
The fridge for example is fairly constant, depending on ambient air temp and fridge type, some are more insulated than others. Here is a link to a worksheet http://www.wholesalesolar.com/solar-information/start-here/offgrid-calculator#applianceTable
Its not perfect by any measure but it is a good way to visualize the loads. I would agree you could probably make due with 4kw inverter, depending on surge capacity. Inverters are kinda like generators, they are more efficient depending on load. With that said 6 Lifeline 8D @ 210Ah = 630Ah @ 24Vdc Depending on how long you want your batteries to last you choose how far to discharge them. Off-grid solar for example for longevity I would say discharge to 70% and the batteries will last many years if taken care of (up to 15 years). However, MOST people will destroy batteries much sooner as the care and feeding become tiresome. With that said, figuring that if you get 5yrs out of a set, you will be lucky as inverters are severe duty for batteries. Especially in an RV situation. I have a similar size battery bank, I plan to use 60% discharge, but will probably go to 50% as I'm realistic about what to expect for battery life. In other words don't choose 70% (30% Discharged) because the batteries probably will not last beyond 5yrs anyway, so you might as well get good use of them. OK, so back to the numbers. 630Ah/ 50% = 315Ah (7560w) to work with. That will certainly power a fridge for two days, throw in the microwave now and again along with some instant hot water... Speculating here, but I think you should be good, as long as there are not too many constant draws. Make sure to put a balancer between the two 12V banks, you will get uneven banks when discharging down to 50% and when heavy loads are used.