ADC+BLE causes unexpected delay

Hardware Nano Family Nano 33 BLE
1

I am trying to measure data from a vibration sensor at 10 kHz and transmit to a central over BLE. I can reach that sampling rate with no problem when I try to transmit it over serial to the computer, but when I start a BLE, even without any connection, I get a lot of delays that cause my sampling to miss the sample deadline. This code visualizes it.

#include <ArduinoBLE.h>

#define T 100
#define BUFFSZ  512

unsigned short buff [BUFFSZ];

const char* deviceServiceUuid = "ab6f99b3-4127-4d63-884a-d19fc6f4e98d";
const char* deviceServiceCharacteristicUuid = "c7600e82-ba43-4f24-82c7-64b0db67abf1";

BLEService audioService(deviceServiceUuid); // Define a service
BLECharacteristic audioCharacteristic(deviceServiceCharacteristicUuid, BLEWrite | BLERead , BUFFSZ);

void setup() {
  // put your setup code here, to run once:
  Serial.begin(9600);
  while (!Serial);
  analogReadResolution(12);
  if (!BLE.begin()) {
    Serial.println("Failed to initialize BLE!");
    while (1);
  }
  BLE.setLocalName("BaboonCollar");
  BLE.setAdvertisedService(audioService);
  audioService.addCharacteristic(audioCharacteristic);
  BLE.addService(audioService);
  BLE.advertise();
  Serial.println("Nano 33 BLE (Peripheral Device)");
  Serial.println(" "); 
}

void loop() {
  // put your main code here, to run repeatedly:
  unsigned long begin = micros();
  int read = analogRead(A0);
  if (micros() - begin > T)
    Serial.println(micros() - begin);
  while (micros() - begin < T);
  

}

I know of a great guide about how to do non-blocking ADC sampling, but using that messes up the BLE. Is there anything I can do or will I have to try a different chip outside arduino?