But you don't have the entire thing on maximum-brightness-white for the entire hour do you? That's why I asked about the duty cycle. If it's on 75% brightness but flashing half the time off and half on and then it only gets to 100% for a minute at the big finale, then you only need 37A of continuous charging capability. The car battery can supply surges of hundreds of amps for several minutes when required.
Or think about it another way: the 50Ah battery will be flat after 1 hour but at the same time you add the 50A charger for 1 hour. This gives you 100A for 1 hour. $45 plus a battery sounds cheap to me.