Every time I check craigslist locally I see several good looking used road bikes weighing in the low 20s for under $300. Some of them could probably be lightened by gradually replacing certain bits: lighter wheels and tires, pedals, carbon seat post/stem/bars/fork, lighter saddle, etc.
Total price after replacing those components will probably bring the final price of the bike up to $500-$700, but at least you'd have a good project bike to ride while replacing bits as the budget allows.
Or save up for a few months and buy a lighter complete bike with the same money.