Back to ChrisD's Post.
With the 1500 Watt induction burner, you will be pushing the 100 amp hour LiFePO4 battery. I would double up to 200 amp hour LiFePO4 battery, then you will have enough. Do you have a monitor? I would put in something like the 700 Victron to the 712 monitor. You want a shunt reading ampmeter, There are chinese copies--I have one which cost about $40 (a few years ago) and is still going strong.
You can "safely" drew a 100 amp hour battery to about its 80% discharge. If you are going to stay off the dock for several days, you can probably keep the battery fairly well charged off an outboard alternator which puts out 40+ amps---10 for the engine, a small aount for the depth sounder and chart plotter. You want a DC to DC charger, where you can throttle up or down the amount of charge to the LiFePO4. battery. I would usually pull 30 amps for charging the Li battery and leave 14 for the motor and other "house needs".
You should never directly combine the Li battery with AGM or Lead Acid battery. There will be a high inrush current to the engine start battery, and could also potentially damage the Li battery. (BMS should shut the Li battery down,) I used an induction burner with a single LiFeO4 battery. I found that medium power (600 watts, measured, input into the induction burner was adequate for all of our cooking needs. However I did run refrigerator/freezer and occasionally a microwave. I had a 1000 watt Honda generator (was better when I had a 2200 watt Honda generator, and would run that when I wanted the microwave. There would be some power "left over" for the house usual uses such as riding lights, cabin lights, maybe the MFD for an hour or so planing your next days trip. I upped the Li batteries (Battle Born), and was using a Victron 2KW/80/50; inverter, battery. You do want to be "safe" charger/boost. The boost function is when powered into mains dock power (or at home if the boat is trailered home, or used as a "boater home" in an RV Park where the mains voltage drops to 90 amps 120 AC, instead of the touted 120 volts. The boost function draws on the Li batteries to combine and syncronize the inverter /charger with mains power. You need to have a large block fues inline right after the battery, and before the on off switch for the Inverter. The Victron acts as a automatic power combiner. I made a separate setup with a 100 amp hour LiFeP04 battery with fuse, transfer switch and Orion battery isolator. I fused for 300. I used a smaller inverter (1500 watt). I used a cheaper Chinese copy of the Inverter and battery charger on thee boat initially. I blew out the switch: That switch arced and blew the fuse, when for some reason the switch failed. This did not fail, when we lost the boat trailer due to the pole tongue failure on the class 3 htich. This "portable" rig has a a 100 amp battery, and the occasionally easily serviced fused at 30 amps
Back to the second setup and 1000 watt inverter, mostly running a "Black Forrest" 35 liter capacity freezer/refrigerator in my SUV. It was portable enough that Marie used it in her Lincoln MKX (SUV) which had a slightly lower capacity.. The use of switch in the freezer which was used on SUV trips only (Pensacola to Culver City Market for my gluten or bringing frozen foods from the nearby Aldi, Publix or WalMart supermarket in the summer heat of Florida, Texas. New Mexico, Arizona, or California summer heat super market. This allowed us to keep meals frozen for over a month, suppliment with local markets for veggies at local supermarkets. When traveling in the SUV only (no boat/trailer) we used this "portable" setup.
You mentoned running a "modest wattage" boat heater. That will drain the 100 amp hour battery in less than an hour. If you run a 1000 watt boat heater, then I would have a minimum 1000 watt Honda to charge the li battery bank in less time.
