Set method to change StartMode property using SqlServer.Management.Smo.Wmi.Service
Hopefully I can answer your question and explain how I did so.

To alter the service start mode using your code above you run

# Check Start Mode
$MyServerObject.StartMode
# Set Start Mode
$MyServerObject.StartMode ='Manual'
# Alter Start Mode
$MyServerObject.Alter()
# Check Start Mode again
$MyServerObject.StartMode


You can establish by using Get-Member as shown below

$MyServerObject|Get-Member


In the list of results you will see

StartMode                Property   Microsoft.SqlServer.Management.Smo.Wmi.ServiceStartMode StartMode {get;set;}   

The {get;set;} shows that you can alter the property

You will also see

Alter                    Method     void Alter(), void IAlterable.Alter()   

This is the method that you will use to apply the change to the object.

You can use the same principle throughout your PowerShell use.

It is also possible to do this remotely, if you have the correct privileges for your account, to do the following

# Get Service                                         
$Service = Get-WmiObject win32_service -ComputerName COMPUTERNAME -Filter "Name = 'MSSQLSERVER'"            
# Get Start Mode                         
$Service.StartMode     
# Change Start Mode                                                                                                                
$Service.ChangeStartMode('Manual') 
#Check Start Mode                                                                                                                    
$Service.StartMode                                                                                                                     


to achieve the same result