If the limitation you're looking to overcome is a lack of heat for large devices, and the inability to regulate and profile temperature, then why are you looking at changing the bottom plate you have?
For a large, costly BGA, the problems I'd personally be looking to solve would be alignment, profiling, and heat capacity, in that order.
It's notoriously difficult to accurately measure the temperature of a hot surface with a thermocouple, due to the poor thermal contact between the thermocouple tip (round) and surface (flat). Do you have access to a thermal camera which you could use to see how hot your device is getting?
How do you place your component accurately on the board without risk of smearing solder paste between pads? A good BGA rework station includes an optical system to help align the pads exactly with the PCB footprint. Is that something you might need, or do you have a very steady hand and/or only use coarse pitch devices?
I use a JBC TE-2A hot air station, which includes the capability to set a reflow profile. You can fit the handpiece into a stand (though JBC don't make one, oddly), then program the base unit to adjust the heat over time. If you already have a hot plate and board holder, maybe something like this would be a good substitute for an integrated rework station?