I'm not sure if I totally understand but it sounds like you want to create a revision system without using the pdm. The system will have two libraries - one for production prints and the other for copies to be sent out (pdfs). And you can't use the pdm - just saying that again since that is the logical thing to do. So you need a whole new process or what are you looking for? Just how big is your department? Specifically wondering how many people actually will make and release drawings?
I was asking that since you might be able to, if there aren't too many people involved, set up a system with just one seat inside the pdm. You (or someone) would have be the person to move files out of release where others would work on them outside the vault. Then you would check them back in, transition them with an incremented revision, and use a task to automatically create new pdfs as the drawings go through. You would then move the pdfs and overwrite the old ones in the second library. At least you could have notifications sent out automatically.
It would be extra work for someone. Of course if you had the extra money to pay someone to do this it might be cheaper to just spend that money on extra seats.
I would like to say from similar experience that if there is any way that you can make use of your PDM now (and Stephen made a good suggestion on it) you should do so. The longer you wait, the worse and more costly it is going to get. Things like that just tend to multiply with time, especially is people get used to it, and one day you will wake up with a massive problem. You will also start seeing things like parts being made to the wrong revision, etc., which can get costly. I did it for awhile using myself to move the files for everyone else across to a series of folders on the network. It did manage to keep our part and assembly files together, but it wasn't that good for revision control - unless you're willing to use up a lot of file space very quickly keeping duplicate records of everything, and then you open up the door to getting outdated versions coming from everywhere.
Sounds like you're in a good spot to think out of the box and come up with a solution before it gets out of hand. Also, that your upper management is onboard with the concept that something needs to be done, which believe me is very good. Given a little time, I would guess that both Solidworks and especially PDM will demonstrate their value to where you might be able to justify the money for additional licenses. At that time, maybe floating network licenses will get you the best bang for the buck, making it more available for less money.
Right now, being the only person who uses PDM, and Soldiworks, the powers that be want me to noly use the free version of PDM. Eventually down the road we will get a few extra seats. This library is such a cluster I have multiple drawings with the similar part #, and all with the same revision.