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You could check out my project BEV. I'm planning for a 50 mile range on my LiFePo 48V pack and it will weigh HALF of what the other SLA E-bike weighed. My budget was $1500 which included everything even helmet and flashy lights.
Weight of lead acid batteries are no joke... an 12V 18aH battery is 14lbs... If you have a 48V system you are talking about a 56lb battery pack! I know that doesn't seem too bad but it isn't until you try to lift it that you realize that is a lot of weight...so swapping out an SLA battery isn't really feasible.
In your situation and only if you are stuck on electric... an electric motorcycle might be a better alternative. I only say that because with a motorcycle frame you can put on more batteries for longer range and you don't have to pedal ever. As for budget... If you could get a complete motorcycle very cheap or free it might be possible to convert it for $1000... You would have to get used batteries and a cheap conversion kit.
Otherwise you should be able to find a small older motorcycle for under $1000.
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