ahh. Little problem possibly.
You mention amps, is that AC amps you are talking? If so then you roughly have to multiply them by 12 to see how many DC amps the battery is going to get hit with. A brewer im thinking 1200 watts plus, that's a 100 amp hit on the battery right there, not to mention what the inverter uses or burns off as heat. 100 amps off a 100aH battery is a 1C discharge rate. The battery is not going to like that very well for the 3 to 5 minutes you are draining it like that. If your voltage sags too much the interter is not going to like that and will probably trip offline. Youd be lucky to get 30 minutes off the battery, being constant, it will probably be closer to 15 to 20 minutes.
If I am correct the steamer simply won't work, you will burn up the battery drawing that current for any sustained time. A few second shot at 4C to start a vehicle is one thing, a few minute shot at 4C is entirely different and will cook it.
Options, go with a bigger battery, VERY bulky and expensive, or two in series for 24 volt, a bit easier to manage but essentially takes up the same amount of room. FWIW a 100aH sla is about 40 to 60 pounds depending on how well it's built and is the size of a group 27 car battery. That's pretty much a full size car battery. also fwiw a group 31 while being bigger is not going to give you significant more ah for the size.,
In your case if it is at all possible, though I am not sure.. id strongly recommend propane. Mount a 40lb tank on the front of your buggy and have a burner on it to heat the water, it would last a lot longer and in your case be much more efficient than a battery source of heat. Easy to fill, several locations to fill it at. Then use the inverter / battery for the juice for the grinder and the electronic part of the coffee rigs. You could probably get away with a 1kw inverter then too, a LOT smaller, and cheaper. and still get away with one 100aH battery. If you had room you could get a 10 or 15 gallon kettle / bucket or whatever size fits, heat it at home using whatever method and just keeping a burner under it at simmer to keep it at the temperature you need.
One other note on the inverter, there are a load of cheap POS chineese knockoffs you can get... DON'T. In this case you get what you pay for fits extremely well. They probably won't last a year. Get a true sinewave too if you can, or at least a fully stepped modified sinewave. Anything else into a motor (your grinder) is asking for problems (unless the thing has a universal motor which i sincerely doubt) and the thing might not even start under load, (ie your grinder has some beans under the burr already and it's starting up under some torque and not into a free spin) .
If you have no way around the power then to be honest, Id have to say you need a generator. (65 amps AC would be 650 amps minimum DC @ 12V, add 20 percent and we are close to 800 A. Your show killer is the steamer there really. A battery bank that can handle that kind of power draw without damage for what you need is essentially a fork truck battery. A 12v model at around 1500 aH which is what you'd need runs about 1800 bucks delivered from GNC (check prices lead changes daily) and weighs about 700 Lbs. Oh and you'd need 4/0 wire for that, possibly even 250mcm at least. that runs a good 10 bucks a foot.
Sorry to rain on your parade but I was not aware the extreme power requirements you were needing.
Aaron