For background, the Link Rail was originally going to include a stop in First Hill, but due to technical reasons, this had to be dropped, and a streetcar from the ID to Capitol Hill through First Hill was proposed. The route (map to the left) will take advantage of the proposed Jackson street extension (map to the right) to the existing Benson Line to cross I-5, where it would go up 12th Street, the up Boren and connect to Broadway. The First/Capitol Hill Streetcar had its plan extended to Aloha street from where it was going to end at East John Street. According to the analysis by Sound Transit, this adds an extra 500 round-trips a day to the 3000 they were already expecting for the East John terminus.
They were looking at about $117.3 – $134.9 million for the East John Street terminus, and according to the email I got back from Sound Transit, extending it to East John adds about $12 million to the final price tag, and extends construction another month. Six blocks a month seems like a bad deal to me, as Portland was able to build one block every three days when they built Max, but everything seems to be slower in Seattle.