HARUKA to Kyoto Station, about 75 minutes. From the Hachijo Exit it is a 15-minute walk, or one Kintetsu stop to Toji Station and about 10 minutes on foot.
Keihan Shichijo looks like the neat answer but earns its place after the temple, not before. From KIX, reach Kyoto Station first and decide the last leg there.
The path is a 2 km walk, not one entrance. After Kyoto Station, choose the Ginkaku-ji end or the Keage and Nanzen-ji end so you do not cross Higashiyama twice.
Haruka to Kyoto Station, Nara Line to Tofukuji, then Keihan to Gion-shijo for the Shijo side. With heavy bags a taxi from Kyoto Station is the better trade.
Kyoto Station is the handoff. Continue on the Karasuma Line to Karasuma Oike, change to the Tozai Line, and leave at Nijojo-mae. JR Nijo is a different station.