Are you sure the lowest wattage oven you can find, can even get hot enough and be large enough for your requirements?
Do not know if a resistive load like a heating element presents anywhere near the start up surge of a compressor or electric motor. My 200 watt lasko heater has no issues on my 400 pure sine wave watt inverter. That is a 18 to 19 amp load on my battery.
Peukert steps in on larger loads, reducing battery capacity.
A new fully charged healthy 100Ah battery can produce 5 amps for 20 hours before considered 100% discharged at 10.5v.
This does not mean it can produce 20 amps for 5 hours.
With a generous Peukert rating of 1.1, a new healthy fully charged 100 Ah battery only has ~75AH to deliver under a 19 amp load.
Under a 30 amp load, about 70AH capacity total.
Most inverters will cut out below a certain voltage say 11.5v or so. Healthy AGMS can usually hold this voltage for longer than healthy flooded, all factors being equal..
Depleted AGMS batteries really lust for higher amp recharges( 20+ amps per 100Ah agm battery, higher than what solar can do practically. LOwer $$ agms say no more than 30 amps per100AH capacity, higher end like Odyssey, northstar, and Lifeline say no limit on charging amps, voltage limited to 14.4 to 14.7ish.
Lesser$$ AGM can likely take more than 30 amps per 100Ah capacity. Monitor case temperature rise. Take notice if it approaches 110f. Terminate. Especially before 120F.
I don't think you can really pull this off for long with less than one group 31 AGM battery, with short fat inverter cables. And As much capacity and solar as you can budget thereafter.
Alternator with thick copper cabling, can satiate that AGM high amp lust, perhaps offset/negate inverter load. A pair of quality 4 AWG jumper cables hooked from engine battery with engine running, to Inverter battery terminals can easily produce 20 amps, and perhaps significantly more.
There will be a large spark hooking up jumper cables, so be aware of that on a hot recently charged or hard worked flooded battery.
Lesser capacity of battery can work,............. but for how long, what are the consequences if you need 30 minutes of oven but the inverter cuts out after 5 minutes?
The key to reliability for acceptable duration, is replenishing the AGM battery quickly after use, and as full and as fast as possible as often as possible. If one can't accomplish this often then they get to replace them more often , flooded or AGM. But agm cost more to kill prematurely and suffer without the high amp recharge more than cheaper flooded.
It's all a trade off.
A flooded group 31 can also accept high amperage, but the AGM would likely accept more from the alternator in the time the engine is running, with short fat copper joining them.
A group31 is the biggest somewhat easily available flooded 12v battery one can obtain at 13x6.75x9.25" tall. It weighs at least 57 Lbs, hopefully more, hopefully no less. If less it is a starting battery, and will not tolerate many deeper cycles.
MOre capacity means more voltage held for longer before inverter can't support load.
AGMs can hold higher voltages for longer than flooded batteries of the same capacity.
More solar means it can partially offset load and recharge faster.
More copper between alternator and depleted battery means much faster recharging to 80% Charged.
80 to 100% is 3+ hours more at 14.4v, minimum. Longer with less than 14.4v and longer when battery is older and has not seen a full charge in several cycles. Sometimes this 'Longer', can take 10 hours, even at 14.4v.
If it does not get this 'longer', its useful capacity lifespan just got shorter. Capacity Decline is then much more rapid.
More Copper between alternator and depleted battery which is powering inverter, means alternator can likely power entire load at idle, or at least much of it for as long as one cares to idle.
When doing this, Watch engine battery voltage Hoping for 13.6v+, worry at 12.8v, and alternator temps should not be allowed to exceed 220f for long. Have an IR temp gun?
If engine battery drops below 13.2v while idling and running inverter load, It is likely providing what the alternator cannot to support the inverters load. So robbing engine battery to power the inverter's battery. Better to keep engine battery bursting full, IMO.
The cooler the alternator is, the better. Movement is good as higher alternator fan rpms and underhood air movement is increased.
So, it's all a trade off.
I'd see if the 300 watt oven can get hot enough and fit your needs on grid power.
If so, and you really wanted to refine how much energy you needed to power it:
http://www.p3international.com/products/p4400.html
But in general, you need more than 50AH of sealed battery, and more than just 100 watts of solar if the system is to have any reliability for any duration.
I use some polymer clay stuff in jewelry-making. I was hoping. Maybe since it's so much smaller than sculpture it *could* work. I'll have to experiment with solar oven when I have one and get a chance.
