The option you are looking for is called in telecom slang “porting a number.” Depending on the new phone service you choose, there might be a charge. I know that the Zadarma Project VoIP service provider allows porting of US landline and mobile phone numbers free of charge.
Take a look at the Zadarma Project internet phone service provider. They have on offer awide range of US virtual phone numbers. They do not charge any for the connection, and the monthly fee is only $2. This is much better than the offers you mention in your post. I also find their service is very friendly and easy to work with.