Two things:
First, if you are transferring torque to the sprocket (i.e. it is not an idler sprocket), you really want to try to get over 120 degrees of wrap on the sprocket. It isn't a hard and fast rule but it is pretty reliable. I've had a number of cases where I reconfigured routings to get over 120 degrees of wrap, chains that were jumpy and poppy and just creeping me out have settled down and I've never had to worry about them again. 120 degrees of wrap. It's a big deal.
Second, it is almost always a mistake not to design chain tensioning into things from the start. You can sometimes get by without it (especially if you can have good wrap angles on all your torque transferring sprockets). Idlers are a nice option depending on your chain routing. I am a fan of moving one of the axles -- even wheel axles which can be done successfully.
My suggestion is that when you use slots to provide your adjustment, do not depend soley on the clamp load of screws to keep your center distances from moving. If you have some slots in a bracket, then have another screw that helps take the load if the screws that are in that slot loosens up. I am doing a terrible job of explaining this.
Here is a photo of the concept on a BMX bike chain.
Finally, chain tensioning by moving center distances is more easily done with dead axles where you can use eyebolts as your adjustment mechanism.
Joe J.