I would build the table with the White Oak leaving the center open except on the two ends.
From the back (underneath) glue and screw 3/4” plywood to cover the opening.
I would overlap into the White Oak 2”. The holes will have to be pre-drilled for the screws into the Oak.
Since the Oak is 5/8” thick, you now have a nice flat 5/8” recessed trough to lay your tiles in.
If the tiles + the quickset mortar is too low, you will need to lay another thin sheet of wood in the recessed trough to build your height to level. For example, if the tiles are only 1/4” thick and with the adhesive you are still only 3/8”, your tile will set 1/4”below the table top unless you build up the opening under the tile. You can use 1/8”, 1/4” or whatever is required to make the center tiles level with the White Oak top. For this filler you can use plywood or MDF.
Please show a picture when completed.
If you don't have time to do it right the first time, when will you have time to do it over?