Generate list based on multiple criteria - list active projects by engineer

I'm trying to generate a list based on multiple criteria. I've followed a guide but it only uses a single criteria. When I try to make a complicated IF statement using AND or OR, it stops returning arrays and the whole formula breaks.

End Goal: list of active projects Bill works on. From Column B (status), any of "Design","Quoting","Feasibility","Post Design" are considered active
Current work: I've figured out how to get a list of internal codes for projects Bill works on using the guide. However, AND() doesn't return an array like IF() does, so saying IF(AND(<bill works on it>, <is active>)) doesn't fit in my formula.
I want to say IF cell[X,I] contains "Bill" AND cell[X,B] is one of "Design","Quoting","Feasibility","Post Design" then return true, RETURN AN ARRAY

Maybe there's a different way to go about it but this is the route I'm taking so far! Please see the attached WorkBook, there's notes in there as well with proxy data and my formulas so far.

Simplified Example of what I want to do in the middle of my larger listing formula:
I generate a 4x5 array of TRUE/FALSE values. I want to create a second array, this one 1x5, that takes the first as an input and OR's each row to into a single column. i.e.:
TRUE FALSE FALSE FALSE
FALSE FALSE FALSE FALSE
FALSE FALSE FALSE FALSE
FALSE FALSE TRUE FALSE
FALSE FALSE FALSE FALSE

turns into

TRUE
FALSE
FALSE
TRUE
FALSE

Thank you in advance!

Thank you both. I used a brute force method where I generated an array to a hidden area of the sheet, and then did calculations based on those cells. Both you you guys have clean formula based solutions Will definitely be fixing mine!

You are welcome, I'm glad to help, thanks for the feedback and rep. .