I found that just moving each individual resource rather than the entire resource group was the answer. Using this script, I can list the resources I want to move in a parameter and move each resource individually through a for loop.

move.ps1:

$locationId                 = $env:locationID
$destinationId              = $env:destinationID
$destinationRg              = $env:destinationRG
$resourceList               = $env:resourceList -replace 's', '' # Remove any whitespace

Write-Host "locationId: $locationId"
Write-Host "destinationId: $destinationId"

# Define an array of server names
$resources                  = $resourceList -split ','

# Specify the target resource group and destination subscription
$locationSubscription       = $locationId
$destinationSubscription    = $destinationId
$targetRG                   = $destinationRg

Set-AzContext -Subscription $locationSubscription
# Loop through each server name and move the resource
foreach ($resource in $resources) {
    $Resource               = Get-AzResource -ResourceName $resource
    if ($Resource -ne $null) {
        # Attempt to move the resource
        try {
            Move-AzResource -DestinationResourceGroupName $targetRG -ResourceId $Resource.ResourceId -DestinationSubscriptionId $destinationSubscription -Force
            Write-Host "Moved $($Resource.Name) to $targetRG in subscription $destinationSubscription" -ForegroundColor Green
        } catch {
            # Handle the error
            Write-Host "Error moving $resource $($_.Exception.Message)" -ForegroundColor Red
        }
    } else {
        Write-Host "Resource $resource not found in $locationSubscription!" -ForegroundColor Red
    }
}

move-reosurces.yml:

trigger:
- main

parameters:
- name: locationID
  type: string
  displayName: 'Where is the resource located?'
  default: '<origin-subscription-id>'

- name: destinationID
  type: string
  displayName: 'Where is the resource going?'
  default: '<destination-subscription-id>'

- name: destinationRG
  type: string
  displayName: 'Where are we putting the resource?'
  default: '<destination-resource-group>'

- name: resourcesToMove
  type: string
  displayName: "What resources are we moving?"
  default: '(Separate the resources with a comma! Ex: resource1, resource2, resource3)'

steps:
- task: AzurePowerShell@5
  inputs:
    displayName: 'Move Resources'
    azureSubscription: '<service-principal-goes-here>'
    ScriptType: 'FilePath'
    ScriptPath: '$(Build.SourcesDirectory)/script/move.ps1'
    azurePowerShellVersion: 'LatestVersion'
  env:
    locationID: ${{parameters.locationID}}
    destinationID: ${{parameters.destinationID}}
    destinationRG: ${{parameters.destinationRG}}
    resourceList: ${{parameters.resourcesToMove}}

This script will do the job.