I recently faced a similar problem. But my mill is not a mini.
Just for starters, your mill has a table that is only 4.7" deep. A six inch milling vise will be at least 8" wide and even sideways, it will stick out a LOT both front and back. And it's Y axis travel is only 5.1" so, even IF you can find a suitable mounting location, there is no way that you can even reach all of that. If you leave some space behind the work piece for an edge finder to operate, you are going to be at around 4.7" of usable Y space. A six inch vise is totally out of place here.
When I recently purchased milling vises (I bought two identical ones, one with a swivel base) here is what I did. I made cardboard cutouts as close to the dimensions of the vises offered from their descriptions on the internet as I could manage. As I said, I have a larger mill with a 9 3/8" x 32 1/4" table with X - Y movements of 7 7/8" and 21 5/8". I was torn between the 5" and 6" vise sizes. Here is what those cardboard cutouts looked like when I placed them on the table.
First the 5" vise size:
In this photo I have used a rod in the mill's spindle to see where that spindle axis hits the vise. In this photo, the vise's mounting lugs are aligned with the second table slot and the spindle axis is just a little behind the fixed vise jaw so an edge finder could be easily used. When I moved the table backwards the spindle axis shifted almost to the line that represented the fully open position of the movable jaw. This told me that I could access almost all of the vise's working envelope.
And here is the 6" vise size:
Again I positioned the vise on the table so that the spindle axis was a bit behind the fixed jaw. But when I moved the table to it's rear most position, the spindle axis was only a bit past the center of that vise's working envelope. You can see in the photo just how far the vise would have stuck out past the front of the table. The six inch vise was clearly overkill for my mill. I would never be able to use all of it's front to back envelope and, after considering the limitations with the table slot positions and keeping the vise from hitting the vertical column, the six inch vise may have even given me a smaller working envelope.
I found that these cardboard cutouts were very helpful in envisioning the use of the two vise sizes on the mill. I was also going to try a four inch cutout, but the five inch size seemed to work out so well, that I did not bother with that size.
Here is the five inch vise on the mill table.
As for the X axis (left - right) envelope, remember that I said above that I purchased TWO vises of the same model. They may not be of the same quality level as a Kurt or other US brand, but the lower price of the Shars vises allowed me to afford this. I did purchase one of the vises with the swivel base which was only a few dollars more and will provide that feature if I ever need it. But the main reason for purchasing two was so that I could mount them side by side on the table for larger work pieces. This will give me a much larger work envelope than any six inch vise could possible provide.
One more consideration: Larger vises are larger in all three dimensions: that incluces the VERTICAL which has not been discussed above. In my experience with mills, you can run out of vertical space (under the quill) just as fast as horizontal space, perhaps even faster. A six inch vise will have a larger table-to-vise bed and table-to-vise top than smaller sizes will. This is a strong argument for the smaller sizes.
PS: From my experience and obvious success in choosing a vise for my mill, I think that the 4" vise size may be best for your, smaller mill. I think that even the 5" vise size that I am using, is too large for a mill like yours. I encourage you to make some cutouts and see for yourself just what things are. You talk about mounting the vise sideways. I can see a lot of reasons against that. I think my two, smaller vise solution is far better than that. It provides a much larger work envelope. And that is the main reason why I choose to buy two identical vises.
On top of that, the work reaches a certain size when the best thing to do is to remove the vise and use a clamp set to fasten the work piece directly to the table. This gives you the best possible work envelope and minimum or no loss of vertical work space.
