Indirect Sumifs with Or Criteria

I'm trying to sum a range of cells across multiple sheets if they meet certain cell referenced criteria. There are some cases where it will be a single criteria and others where it will be either or.

I can get single and multiple criteria to work with direct sheet reference but I'm trying to avoid having a long formula with several sumifs added together. I tried using indirect and I can get it to work with a single criteria but when I use two criteria the result is wrong. The criteria and sum ranges will be the same on all sheets.

I've attached an example for reference. Oh and this has to be an xlsm file because it links to an database. Any help would be appreciated.
Thanks,