I thinks you’re way over estimating your wattage, i think 250w is probably a sprint but 50-100w is more likely sustainable. Unless you’re talking about a tour d france type athletic effort and fitness level 1000w is absolutely un realistic. At 100v your probably going to be in the 1-4a range. Putting that through a charge controller, a bms, fused and rectified at 90% efficiency seems more doable. The efficiency losses will give you something resistive to push against if the bms is cutting off charge or charging controller is rejecting the supplied voltage. If you put a small super cap bank after rectification it could act like a buffer sucking up your messy generation maybe?
All this is a fun thought experiment but I imagine it sucking and providing little useful watts because of conversion and complication - wouldn’t just peddling and throttling less do the same thing for less effort and translate to more usable range? Get cold - slow down and peddle hard for a minute. If the gearing is too slow to be a useful speed then change your sprockets to a more appropriate ratio