In lieu of a LASER rework station, we use titanium heat-sinks and heat-shields.  In more difficult cases, the shields are coupled with an aluminum or solid copper heat capture block place on top of the component.

For the process:
Pre-Heat the entire assembly to 65C -75C (150 - 170F ).
* It is always a good idea to pre-bake any assembly being BGA reworked.  The closer in time you can be from BAKE to rework, the better.  That is, don't let the assembly cool down if possible.

Form a finned heat-sink out of 0.5mm (.02 inch) to place around the part being reworked.
* Onlinemetals sells 12 inch by 12 inch sheets of 0.5mm thickness for under $40.00.

For the more extreme cases, especially if you are fighting a heavy ground plane, place a cut square of copper or aluminum on top of the part you are reworking, then start your rework process.  The copper or aluminum on top of the part will heat saturate and slow down the thermal transfer into the ground planes.

If you have access to them, use your solder samples to try several different methods and thermal couple all around the part to see where you end up thermally.
Purchasing Tip:
1) Ask the PCB supplier for all failed PCBs for process development.
2) Also, If you know you are processing very small volumes, ask the PCB supplier what the Minimum Order Quantity (MOQ) is.  If the MOQ is greater than the needed quantity, have Purchasing buy the PCBs as a lot and then piece price the buy by dividing the lot price by the needed qty.  All the extras are actually functional PCBs which can be used for process development or replacing any 'Oopsies.'