I ran into a similar problem with a descending note run that had two quick notes back to back on the 5th and 6th strings on same fret (3rd fret) on a song I was learning to play.
The problem I was having before I learned to overcome it was when I barred the 5th and 6th string as part of a fast run, I was inadvertently hammering on the 6th string and the note played before it was supposed to (before I picked it).
So for the longest time I tried rolling the barre finger from the 5th to 6th string, but as you said, it felt sloppy.
So the best way I found to hit those two same fret notes on 5th and 6th string in a quick run without letting the note on the 5th string continue to ring - is to mute the string by lifting up the barre finger slightly between the two notes.
The feel is like a little bounce with your barring finger or pulsing motion. As soon as you pulse mute, the note stops ringing so you don't have to keep it muted. You can also try palm muting the 6th and 5th string or a combination of the two types of muting by slightly pulsing the fretting finger while applying a little palm mute.
The palm mute is indicated if the 6th string note is sounding as a hammer on when you fret the 4th, 5th and 6th strings simultaneously with a mini-barre.
It's probably easier for you to do the barre on the ascending part of the run because it's easier to roll your finger down than it is to roll it up. Rolling down is just a slight natural rotation of your hand. And in the process of rolling your barre down, you are automatically muting the previously played string as the top part of your finger comes up when you roll the barre down.
It may take a little practice to get the timing of the pulse muting just right (at least it did for me) but I spent a great deal more time trying to roll my barre finger up (awkward) and never did get that working smoothly.
Hope that helps. Good luck.
PS: not for Rogerio or experienced guitarist who know better - but for future readers who may be just starting to learn guitar - when we say descending part of the run - we mean notes getting lower but fingering moving closer to the low e string and when we say ascending, we mean moving down towards the high e string. Notes are ascending but fingers are "descending" towards the floor to play "ascending" (higher notes). Some folks who are self taught at guitar seem to get this confused sometimes.