After some considerations I decided to make two small modifications. One for the fixed end gripping mentioned above and the other was to make the fixing bolt pockets a little larger than the original ones.
Fixing new vise jaws
It was a really satisfying feeling to watch the aluminum chip spray flying away from the tool and to see the results when the machine stopped. The pre-milled jaw pairs were also fixed on my CNC to get them as good as possible.
The bolt pockets
Once everything was as good as I could make it, I assembled and installed the vise, squared the sides on my CNC table and made another final milling run on the jaws to make them absolutely parallel, or at least as good as I could make it. I measured the parallelism error to 0.003mm from one side to the other, over a total width of 140mm, so that is 0.0214mm per meter error, which is good enough for me.
For those who are interested, here is a short video about the modifications I made.
This was the first time I milled aluminum with my upgraded DIY CNC. I am a bit surprised with the results, very satisfying and nice in my opinion. I know some people will disagree with me, but I will continue dry milling aluminum without any lubricant. For now, I see no problems with dry milling. Of course, the speeds must be right, but it seems to work just fine. Perhaps tool ware is much worse, and perhaps the results would be even better with lubricants, so it is a compromise, but at least I don’t have to handle chemicals and inhale the fumes.