1,2. I am not sure how exactly you made timing measurements, so accuracy is not so clear.
I would say that relocation time should be absolutely the same in either case, just because the time is defined by the slowest device (i.e. NOR flash) and this device is always the same.
On the "default" P4080DS it takes about 120ms from MEM_EN=1 to D_INIT is cleared for 1GB memory size, so for 2GB it takes about 240ms. As I understand this matches some of your measurements.
3. D_INIT=1 is used to overwrite the whole memory in order to initialize ECC. By default, ECC is disabled on the P4080DS. If it is so in your case, you can simply set D_INIT=0 in the u-boot to exclude ECC initialization. This would significantly reduce initialization time.
4. As I can see in the documentation we never stated that the user needs to wait for D_INIT.
Regards,
Bulat