OP needs to research each Honors program. Too many assume 100% of academics are Honors. Often it’s far far less and sometimes additional classes vs major or required classes.
So yes but they should then research each and every. People tend to paint Honors with one brush and it’s many brushes.
Lots of smaller schools will meet their budget, academic and geographical needs as originally stated but yes they did note that as you point out. But most seem to be larger that are recommended or outside the NE.
Only reason I pointed the reminder. Hopefully folks can recommend schools to hit the desired targets.