Why is BLE your choice for converting your project to wireless? Trying to generate large packets and arranging for larger MTU's supported on both client and server is heading down a different path from the short energy saving transmissions BLE was designed around.
I also reviewed the BLE Specification in the nRF52840 and found the maximum recommended BLE throughput is 1Mbps.
I think this is a radio transmission rate.
Here is a good article on the BLE maximum throughput.
https://www.novelbits.io/bluetooth-5-speed-maximum-throughput/