I have a few random comments from someone who lives full time in an RV with a big inverter and a battery:
The 120V induction cooking elements are underwhelming if you are used to a regular induction or gas element at home. Think 1500W versus 4500W. Still, they work okay if you are patient. They are about 25% more efficient, which is nice but probably not an energy budget game-changer for most people.
You say you are heating with a woodstove and maybe some small electric space units. A well-insulated modern 45-foot RV with double-paned glass windows will require something on the order of 3kW average power, continuously, to hold 66F internally with an outside nighttime temperature of 38F. (In reality with sunshine the load is weighted to the nighttime, of course.) So you are going to need a nice pile of wood and maybe some blankets for your adventure, if you are not willing to burn propane, diesel, or gasoline for heat.
You mention electric water heating. Water can be heated at 400degF-gallons per 1kWh with a heater delivering 100% efficiency. Those small heaters typically are often sized for 1500W so they can be run on a typical 15A 120V residential circuit. Plan for about 1kWh per conservative, camping-style shower.
If your bus basement is reasonably insulated, and especially if you place your water heater in it, you may not ever need to run an electric blanket to keep your batteries from going below 32F. They have a huge thermal mass and will prefer to stay close to the mean internal temperature of the basement rather than swinging much.
Conversely, we know that maintaining lithium chemistries at temperatures exceeding 100F is deleterious to their health (regardless of other variables like SOC which also impact lifetime). It could be difficult to keep them cool when parked or underway on warm days on hot asphalt. This should be a real design consideration for you.
You describe being able to fit about 3kW of PV on your roof. You should expect something like 18kWh of energy from that setup on good days. The panels will derate as they warm up, and you won't get perfect tracking, and you'll not always be at the equator. You should expect you could have a whole week with effectively 0kWh. What will be your plan in these cases?
Camping in the sun is great in milder weather. When it's truly hot, the energy you get from the panels won't offset all the passive heating you'll receive in your rig. Just moving air with fans will help some, but your rig will still heat up. You and your family need to be comfortable living in that reality, or you should consider moving to the shade like the rest of us.

You say you arrived at an 8kVA (inverters are typical in VA, not W) by summing the worst-case scenario for consumption. On the one hand, I suggest you revisit that with more care and caution, and see if you really need that large a system. It is unlikely you would have all the loads simultaneously. Moreover, any big quality inverter has substantial headroom and can absorb peaks above the rated continuous power for a short while.
On the other hand, most inverters are rated in a perfect 75F environment, and you may not be able to maintain that with only fans in an enclosed space on warm days. So, oversizing may still be a good idea.
While I'm a strong believer that you should have the freedom to make your own choices and live with the consequences, I encourage you to think very carefully about using cobalt-chemistry lithium batteries in a mobile living environment. If you have any children or animals who might inhabit your space, they may not have the same ability to exit quickly in the event of a runaway. Egress in general is often a compromise in RVs. There is a reason most boaters and many of us RVers elect to use iron phosphate (LiFePO4) cells despite their higher cost, lower densities, and bigger hassle factors. Be sure you have fully assessed that tradeoff and are comfortable with the additional risk before you proceed with a large system.
Good luck!
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