Trek 1000 (aluminium alas) in 61cm pick up in Beacon NY @
300 USD
https://www.ebay.com/itm/20394751543...oAAOSw-NRicwXz
Approximately 90 minutes drive from Southern CT University
I am not keen on aluminium myself but I like integrated brifters, and you will be unlikely to get steel or carbon with brifters within your budget. You may be able to hold out for a aluminium/carbon bike, as I did recently, but if you put a long carbon seat post and long carbon stem on this bike (I think you will need long ones to make it your size) then they will flex and reduce road vibration.
I sent a message to the ebay seller to ask the height of the rider. The seller responded
6' 3" with 30" inseam. The stem is already pretty long but you can raise the saddle a bit, with the right seat post 2 more inches (though you probably only need one). The longest stems are generally 150mm. It may have a 150mm on it already. My guess is its a 140mm. I am not sure how long and low you like to ride but if you were to flip that stem so that it slopes down it would have the effect of making the reach a couple of inches longer.
Entry level road bike with brifters
I have been able to purchase full carbon with brifters within your budget by waiting but with the added restriction on frame size, you'd be waiting a long time. If you are happy with gear change on the frame, then I would recommend a steel bike such as those below (which have the gear shifters at the top of the steerer tube).
https://www.ebay.com/itm/26442360513...gAAOSwQ8ZgCxxP
https://www.ebay.com/itm/25478046018...QAAOSwwrRh14mo
If this seller could be persuaded to ship from California then it would be my choice but it (as the others) may be too small. Did find out the size of frame you need?
https://www.ebay.com/itm/29450497710...YAAOSw3VlhfCPa