I was able to run a 1000w inverter clamped to my truck battery with 16" lengths of #1 gauge wires, but only if the load on the inverter was about 600w (a 35amp Vector battery charger)---answer follows how to use that instead of the OP plan which looks dubious.
If the load on the inverter got much more than that 600w the truck's voltage would drop off (needle drooping to the left instead of straight up) but it did ok for over an hour with truck idling (do turn off the climate control! That helps. :( )
You can run a small microwave on an inverter but my Xantrex 1000w inverter only runs the Danby 700w one with the inverter showing "overload" at 1050w, which it can do for five minutes before shutting down to cool off. So you need a bigger inverter than that.
That is with the big enough inverter on a big enough battery bank and wiring to be able run 100amp draws.
Your two 27s could briefly if they start out near full, but the alternator supply to the bank on a long #6 would have to supply an increasing proportion of the 100 amps and IMO would very soon run out of steam where the truck's voltage drops off to its starting battery's voltage, which will then fall, and you are losing. So--
You could do it this way--run the microwave off a big inverter properly wired to the two 27s. AND have another inverter up by the truck battery with a long 120v extension cord back to the battery bank where your 35amp Vector is clamped on. With the truck idling it can support that much load no trouble, same as mine did.
So now the 35amps is helping with the 100amp draw on the 27s leaving the net draw at 65a. So now it all depends on how long will the microwave be on before the 27s get down to 11 volts and the inverter alarm goes off?