I have done this and I let the callers know immediately that we will have vacancy soon but nothing currently.  

Most of the larger PMC software providers provide call center options which can be used solely for after hours or emergency.If you want to do it on your own, suggest setting up your phone system so that after hour callers are given an easy option to "Press x if this is an emergency" and are transferred to a specific voicemail greeting.

Hi BP Crew,First time caller, long time listener and new BP member here. 

One caller asked if we'd take $300.

The system administrator can later view the calls placed using each code.Anonymous Call Rejection: Your business will not receive calls unless there is a Caller ID number from the caller.Automated Receptionist: The Automated Receptionist will answer incoming calls to your business and allow the caller to select which department or person they wish to speak with.Automatic Callback: Automatically redial a busy number until it is available.Bridge Line: You can allow your number to ring on one additional desk phone.Call Forwarding: Keep your business in touch with callers by automatically forwarding incoming calls to the best available resource.

Is it truly a cold call or did the other party indicate they want callers? 

You mentioned you send your callers to a pre-recorded message.

I tell my cold callers to rotate the phone number every calling hour, and yes, just like @Eliott Elias said, if your numbers are whitelisted, you'll achieve a better contact rate.

I would like to be able to tack callers meaning that I would be able to know from what list or from what marketing campaign the caller is calling me from.

My thoughts...It doesn't matter... if the phone rings, answer it...If you can't answer it, spend the money and hire an answering service where a real person talks to them from a script you provide gathering the info you need prior to calling them back.It doesn't matter what you say, you're going to lose callers, a LOT of callers, the moment it goes to voice mail.