So given your limitations, fly into KIX and take the Haruka train straight to Kyoto for 3 nights, followed by the Shinkansen to Tokyo for 3 nights. With this itinerary, it is not economic to get a JR pass, just pay for the shinkansen tickets directly.

If you feel up to a cross-cultural experience, you can find a "coupon shop" in Kyoto where you can buy coupons (for cash) that will save you 2-10% on the shinkansen ticket, depending on whether it is Nozomi or Hikari.