Thanks for your suggestions, everyone! I ended up going with the Shimano Tourney STI shifters, a new 14-28 freewheel and chain. I would have bought the Micronew shifters that were suggested, but the shipment was estimated to take over a month. I found a shorter gray anodized Cinelli stem (on a weird $20 franken-Fuji I got recently with some fancy gray anodized Dia Compe brakes and matching levers), so with the shifter install, I'll take the opportunity to swap stems and put on fresh bar tape.