Any other suggestions?  Or, maybe mini-ITX is the way to go and you can
suggest a cost-effective wholesaler or something?

Mini-ITX tends to be a premium-priced thing because it's cute and all-inclusive.

 

Why not get a bargain-basement Sempron on a regular micro- or full-ATX mobo.

 

I'd think an ideal solution would be some old Socket 370 slow Celerons.  You can slap beefy Socket A heatsinks on and run them fanless for reliability.