I know EXACTLY what you mean, by the tilted scan. I had the same problem with my Epson 1260 scanner. The new driver for the scanner does not work; it produces the tilted scan, as you have found out. The old TWAIN driver is no longer supported by Image Capture or any of the apps that run its engine (i.e. Preview).
Fortunately, after several days of trying to fix it, I found a solution. Use the old TWAIN 5.75A driver that you had used with your previous Mac. It will be in the folder /Library/Image Capture/TWAIN Data Sources. Copy that folder and its enclosed file "EPSON TWAIN 5.ds" to /Library/Image Capture on your new Mac. You can also download the old 5.75a driver
here.
Then download Graphic Converter and install it. After it is installed, right-click its icon, select Get Info, and set it to open using Rosetta Mode.
Then open Graphic Converter. Under the File menu, select Acquire -> TWAIN Acquire. You should then be able to scan using the old TWAIN driver you are used to.
It works for me anyway - perfect scans every time, with no horizontal hold problem!