Sizing up a battery bank for max continuous power draw
I spent way too long thinking I was going off-grid and then didn't, as the system cost to do what I needed and the grid connection cost crossed paths when the power company had a slow-down in new connections and got suddenly reasonable...

305 Ah battery is going to have a C/20 rate of 15 amps, for roughly 183 watts on a 12V system. C/20 is the discharge rate over a 20 hour period and is typically how the "305 Ah" is rated in the first place (you get more Ah capacity discharging slower and less discharging faster - and the Ah tends to drop from rated capacity as the system ages.)

A good "rule of thumb" on (lead/acid) battery bank size to support a certain draw is to stick at or below the C/20 rate. If your inverter supports multiple input voltages, I would strongly suggest going to a higher voltage (24, 36 or 48V) since maintaining a battery bank charged in parallel is much more prone to problems than a series string. 

Or, get a different vacuum, or a non-electric sweeper. You don't provide details about your vacuum cleaner, but many are quite high Amperage draw at 120V (or 240V), which will be more than 10 times (or 20 times) as much draw at 12V (inverters are not 100% efficient.) That will result in a very significant increase in the size of the battery bank you need. Alternatively, you fire up a generator for 15 minutes once a week to meet your 10 minutes once a week of high power draw, and haul fuel for it, and maintain it.