This is not so hard, interpolation is simple, but question is to do an interpolation with what.
First, find nearst point on curve closest to your block, then find same thing on the opposite side. You have bearing from block to nearest point, reverse that angle and shoot a ray, then find intersection that ray with other pline's. Take nearest and you have three points for interpolation.
Something to speed up: if polyline elevation (where nearest point is) is 100 m, then build selection set from polylines at elevetion 99 or 101, depends on equidistance.