If you do try to use the NPCs on schools that require his information, be sure to include his finances in the NPC. The result may be less accurate than for simple financial situations, but you do not want to make the mistake of using only your information on the NPC of a school that requires his finances, which will give an inaccurate wildly optimistic estimate if he has any (particularly high) income or assets. Of course, if he is uncooperative with forms (may be due to not wanting to leak his finances to you), then that closes off any financial aid from those schools.
https://profile.collegeboard.org/profile/ppi/participatingInstitutions.aspx has a list of CSS Profile using schools; the fourth column indicates whether the non-custodial parent finances are needed (but verify on college web sites). Of your list, the following require non-custodial parent finances: Stanford, Princeton (own form, not CSS Profile), MIT, Harvard, Carnegie Mellon, Penn, Cornell, Duke, Boston College, Case Western, Lehigh, Reed (an odd choice for CSE…), WPI, Johns Hopkins, Northeastern, and WUStL. This leaves only RPI, Cal Poly (no out-of-state FA), Olin, Santa Clara, ASU, UT Austin, and Texas A&M that do not require non-custodial parent finances.
Reach level schools that have good financial aid and do not require non-custodial parent finances are Chicago (CS, no engineering) and Vanderbilt.