Then you have to buy propriety side clamps that press into the sides of the work-piece and exert a downward pressure, you can also design them yourself, it's old technology.
If you have the room you can make up blocks to clamp to the table and use an M20 tapped hole with a bolt. Drill the tapped hole slightly downward, say 5 degrees and the bolt will pinch and press into the side of the work-piece, place adequate stops on the work-piece and make sure when you side clamp to shim so there is no bending introduced at that point. use a small diameter face mill rather than a large diameter,say 75 mm or 100 mm and take 1mm depth of cut at an insert loading of 5 thou per tooth per rev. Machine 316 around 100 metres peripheral speed. For final machining reduce the insert loading to 2 thou per tooth.
Use a suck it and see approach, if this loading and depth of cut works with no chatter or movement then you may increases the depth of cut. If the billet of steel is not very heavy then grinding is the best approach even if you have the additional cost of sub contracting out.
It is possible to purchase proprietary brands of side clamps similar to a vice, that you clamp to the bed with an adjustment similar to a one sided vice. Buck and Hickman may have them.
I hope this has been of help and can't think of any other advice to offer.