Someone with more familiarity with your model will probably chime in but I would note a coup[le of things. If I were considering doing this, especially on a "lite" trailer, I would cut a piece of 3/4 plywood the size of the entire area of the floor and install it over the existing floor. I think that would add some rigidity to the floor and disperse the weight.
That is an enclosed area and therefore not ventilated for a wet cell flooded battery. You would need to properly ventilate that space or use batteries that do not require ventilation. Those batteries have a markedly increase in cost but also performance and depending on the battery may require a different converter to charge them,
Have you considered 2 six volt batteries on the tongue and and solar panels to charge them. Maybe if you share what your goal is would help with folks giving you suggestions.
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Marshall
2012 Laredo 303 TG
2010 F250 LT Super Cab, long bed, 4X4, 6.4 Turbo Diesel
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