Right, further update from me after more testing today.
I tried the modification with one film holder, as suggested. Well, the modification was successful, but there's a new "issue": The wet sheets tend to stick together (I tested it with HP5+). No issue with development, but the adhesion makes removing the sheets from the holder almost harder than from the unmodified carrier.
And further update on the streaking: Against what has been posted, it does NOT stem from the wetting agent, it is mechanical damage to the film. I can see the familiar streaks on the remaining sections of the film holder which were not cut out - even though I removed the sheets from the tank to perform the wetting agent treatment in an external tray.
Since I mainly use Ilford film I have not yet tested the performance/issue with other brands but for now I will have to refrain from using the tank with Ilford films going forward. Even though the streaks don't show up in scans, I like to avoid as much damage to my negatives as possible, you never know how issues might accumulate over time with increased handling once I finally get my 4x5 enlarger...