Focus next field by tab number after committing using Enter

I have some text fields which act as lines. I have to do this because the line spacing does not match up for the font size I have chosen. I do not want to change the font size nor the lines' spacing. I have not found a way to change a text field's line spacing reliably.

What I would therefore like to do is focus the next line (text field) when the user commits their input using the Enter key. Solutions I've found online use some strange work-arounds and have not worked for me so far. The OnBlur event fires only when the field loses focus using the Tab key or the mouse buttons, not when the Enter key is used.

My idea was to get the current field's tab number and simply change the focus to the next-greatest one when the user hits Enter. I haven't been able to find any API that returns the tab number, nor one that gets a field via its tab number, which is incredibly strange. I would like to avoid having to specify the explicit field name every time.