You cant do that. If you remove the MX record from Microsoft's Office 365, then you wont get mail on your 365 system
You should keep your mx records pointing to microsfot, and set your domain to a shared domain and split the mail off to the other company. At least this way, all your mail for the whole domain will get the use from the Forefront spam filter. I am sure that the "Free Webmail" you are getting from that other company has 0 spam/virus filtering. So that means that all spam/viruses will be delivered to your mailbox.
I really do not see what this "Urgent" matter is...You want Microsoft to help you move away from them. I would think that this "Free" company you are going to should help you move to them.
Remember, you get what you pay for.