Re: Tack reducer
The thin vs thick is very subjective topic. What would be thick in oil paints is thin in printmaking inks. I have had exactly the issues that you mention when I had too thin or fluid inks. Such inks lack the tack that is necessary to keep the paper in place and to roll an even layer of ink on the block. Adding tack reducer or wiping compound will make things worse. Personally I use the thickest of Charbonnel inks just because those are easier to work with.
Another thing might be that there is not enough ink on the block. Adding tack reducer will make it more difficult to roll enough thick layer of ink. Increasing tack (magnesium carbonate) will make it easier to roll enough thick layer. Thick ink will also help to avoid ink seeping to the cuts in the plate.
Tack reducers don't cost a fortune, so I would recommend giving it a try if you are interested to test it. Just remember to follow the maximum ratio of reducer to ink to avoid problems. Another option would be to use the safe wash oil medium to get similar effect with less risk that it will ruin the image.
It is quite rare that inks would work perfectly right from the tube or jar, so it is good idea to have printmaking oil medium, tack reducer and magnesium carbonate available so that you can adjust any ink to fit your printmaking style. Many ink connoisseurs mix different kinds of black inks to get even further tailored characteristics, but that is often necessary only in intaglio and litho techniques.