I cannot speak specifically to your situation as I have not read your property management agreement. However, I will give you feedback based on how I conduct business. I am a Property Manager providing services here in Santa Clara Valley. First thing to remember is that you cannot just go and cancel the existing lease. Tenants have a lease and regardless of your relationship with your property manager, you are bound by it.
That being said, this is how my contract works. If I were the Property Manager and my contract was on a month to month, a new lease with the tenant that just started in May and you decided to terminate your relationship with me, you would not owe me any money from the lease. I get paid only for the months I managed the property and as long as I got a full one month notice, that would be fine. Lease goes with the tenant and property.
This is why it is imperative that you read your agreement to make sure what your liability may be. If unsure, as previously menmtioned, you can check with an attorney. However, you can also ask the property management directly and see what their response might be.
You can change your property manager, as he too is on a month to month.
Unless of course when you signed a PM agreement there was a fixed time period of
2-3 years stipulated.
Give him a months notice and after that either manage it yourself or find a new Property Manager.
You, by definition will never have a month where the PM Agreement expires at the same time as the Tenant's Lease.
You are not under Contract with the PM, (I understand) now, so now would be a good time as any to change.
You can and should expect excellence. Go for it.
Good luck and may God bless
All the best to you.