The word 'restart' had me thinking that it would just immediately start the timer again, but it turns out that is not the case. If the reload was set false previously, the timer has to be set again before it will actually execute - which works perfectly for my use case. Below is my new code (figured I would include the wifi and mqtt stuff to help anyone else as well):

#include <WiFi.h>
#include <PubSubClient.h>
#include <Wire.h>
#include "VCDevices.h"

hw_timer_t * motorTimer = NULL;
Motor linMotor2 = Motor(pulsePin, directionPin);
int d = 0;
bool nextRun = false;

const char* ssid = "SSID";
const char* password = "PASSWORD_HERE";
const char* mqtt_server = "MQTT_SERVER_HERE";
WiFiClient espClient;
PubSubClient client(espClient);
long lastMsg = 0;
char topArr[50];
char msgArr[100];

portMUX_TYPE timerMux = portMUX_INITIALIZER_UNLOCKED;

//Timer ISR
void IRAM_ATTR motorInterrupt(void) 
{
  portENTER_CRITICAL(&timerMux);
  noInterrupts();
  //check if the motor is in motion still
  if (!linMotor2.getMotorStatus())
  {
    d = linMotor2.Update();
    //give timer different delay, dependent on its current speed
    timerAlarmWrite(motorTimer, d, true);
    timerAlarmEnable(motorTimer);
  }
  //kill the timer and interrupt if not
  else
  {
    nextRun = true;
    //set the 'reload' boolean to false, to get it to only trigger one more time
    timerAlarmWrite(motorTimer, 10, false);
    // Serial.println("POSITION REACHED!");
  }

  interrupts();
  portEXIT_CRITICAL(&timerMux); 
}

void reconnect() 
{
  // Loop until we're reconnected
  while (!client.connected()) 
  {
    Serial.print("Attempting MQTT connection...");
    Serial.println(mqtt_server);
    // Attempt to connect
    if (client.connect("ESP8266Client"))
    {
      client.subscribe(motorControlTopic);
      Serial.println("connected");
    } 
    else 
    {
      Serial.print("failed, rc=");
      Serial.print(client.state());
      Serial.println(" try again in 5 seconds");
      // Wait 5 seconds before retrying
      delay(5000);
    }
  }
}


void setup_wifi() 
{
  delay(10);
  // We start by connecting to a WiFi network
  Serial.println();
  Serial.print("Connecting to ");
  Serial.println(ssid);

  WiFi.begin(ssid, password);

  while (WiFi.status() != WL_CONNECTED) {
    delay(500);
    Serial.print(".");
  }

  Serial.println("");
  Serial.println("WiFi connected");
  Serial.println("IP address: ");
  Serial.println(WiFi.localIP());
}

void callback(char* topic, byte* message, unsigned int length)
{
  Serial.print("Message arrived on topic: ");
  Serial.print(topic);
  Serial.print(". Message: ");
  String messageTemp;
  String response;
  
  for (int i = 0; i < length; i++) {
    Serial.print((char)message[i]);
    messageTemp += (char)message[i];
  }

  Serial.println();
  if (String(topic) == String(motorControlTopic))
  {
    if (messageTemp.toInt() > 0)
    {
      //check if motor is available to run
      if (linMotor2.getMotorStatus())
      {
        
        linMotor2.MoveTo(messageTemp.toInt());

        //set the motor timer and enable it
        timerAlarmWrite(motorTimer, 1, true);
        timerAlarmEnable(motorTimer);
        
        response = "moving to " + String(messageTemp.toInt()) + " mm position";
      }
      else
      {
        response = "motor is busy - wait for movement to end!";
      }
      Serial.println(response);
    }
  } 
}

void setup()
{ 
  //Start serial connection
  Serial.begin(115200);

  //Setup wifi and mqtt stuff
  setup_wifi();
  client.setServer(mqtt_server, 1883);
  client.setCallback(callback);

  //Fix up motor settings
  pinMode(pulsePin, OUTPUT);
  linMotor2.SetSpeed(200);
  linMotor2.SetAcceleration(10);

  //Initialize timer here for later use!
  motorTimer = timerBegin(1, 80, true);
  timerAttachInterrupt(motorTimer, &motorInterrupt, true);
  Serial.println("TIMER SET!!");
  digitalWrite(pulsePin, LOW);

}

void loop()
{
  if (!client.connected()) reconnect();
  client.loop();  
  portENTER_CRITICAL(&timerMux);
  vTaskDelay(500);
  count = linMotor2.GetPosition();
  Serial.println("POSITION: " + String(count));
  if (nextRun)
  {
    noInterrupts();
    timerRestart(motorTimer);
    Serial.println("*********TIMER RESTARTED!******");
    nextRun = false;
    interrupts();
  }
  portEXIT_CRITICAL(&timerMux);
}