[SOLVED] Teaching Assistant; letter from my university

[Naturgrl]

And then should I try getting those LORs from more than one professor and my PhD senior as well if that could compensate for the lack of job reference letter from the Institute?

You need proof of your job responsibilities, time worked and salary so any letters from advisors and your superiors will be required if your employer will not do it. Your advisors need to provide contact information.