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If the shuttle expends it's remaining onboard fuel in an all out effort to reposition itself into the deepest (?) orbit possible (under the circumstances)

The Shuttle has no more than about 200 m/sec of delta-V available, which translates to about 1.5 degrees of plane change. The ISS propulsion capabilities are similarly limited.

Even supposing that this was possible, actually changing the ISS inclination to something like 39 degrees makes it unreachable by Russian launchers.

By far the cheapest and most efficient way to reach a Shuttle that is stranded on-orbit would be from the ground -- one need merely wait for the Earth to rotate to the right position, and then launch into the proper inclination. This saves hundreds of thousands of pounds of propellant costs.

The downside to any generic rescue vehicle approach is that you've got to have it ready to go on short notice -- a very expensive prospect in its own right.

Actually, the solution is rather simple.

Before any shuttle is launched with a regular payload, the next shuttle to be launched is prepped with a CRC (Crew Recovery Capsule) in the cargo bay.

The CRC would have seating for 8; food, water and air for 3 days; a quick connect com link to the shuttle; and an airlock for spacewalks.

Once the mission shuttle is deorbited, the "ready" shuttle is moved back to the Vehicle Assembly Building and the regular payload is mated. This shuttle then becomes the primary mission shuttle and the next shuttle becomes the "rescue ready" shuttle.

The cost of the CRC would be very minimal, compared to other shuttle projects. The only cost imposed would be having to have 2 shuttles and 2 launch pads ready simultaneously. plus the 50 million or so for the CRC.

In the event of a major shuttle accident, the "ready shuttle" would be launched into the same orbit as the stricken shuttle. Crew members from the "rescue shuttle" would transport spacesuits necessary for EVA. Rescued Crew members would enter the airlock of the CRC, strap in and wait on de-orbit.

The rescue shuttle would then de-orbit with the rescued crew in the CRC.