Have you played with LiFePo4, especially the bigger cells, and brand new cells? You might be surprised how lightweight and how much less volume they have, compared to the same capacity as lead acid . My guess is that the same weight of LiFePo4 would give you maybe 4times the range of lead. The reason is that with LiFePo4 you can really use 80% of the capacity where lead will be destroyed very fast if you do this too often.
What you might wish to stay away from is second hand LiFePo4 from Aliexpress or Lazada. These cells are half dead and each cell is different from the others, resulting in need for heavy balancing. But new CATL or similar brand cells directly from China are a good option and the price has dropped significantly.
If the vehicle can run on lead acid, it can run on LiFePo4. With double the capacity of the LiFePo4 (because they are smaller and weigh only half) , your current draw would not stress these cells to a level where cooling is required. If this was the case, then your lead acid would already be boiling.