C102/C202 need to be boutique-ish electrolytics; you can bypass them with other caps - PIO might not fit very easily, but anyway... the parts in your list will work, but might not fit very well - the board has holes for 15mm caps with 7.5mm lead spacing, and I think yours are 12mm caps with 5mm lead spacing.
C103 is the power reservoir - low ESR electrolytic, bigger is probably better, all other things being equal. The board will accept a 20mm part with 10mm lead spacing; the part in your BOM is a 16mm part with 7.5mm lead spacing.
C101/C201 are a spot where it would/could make sense to use boutique film caps, like PIOs; I can confirm that K42Y-2s will fit, though it's tight.
Everything else, at first glance, looks like it'll probably work just fine.
$83 USD, huh? (Really more like $103 or so once you figure in shipping, alas.) Didn't realize this was such a pricey undertaking; I guess the fact that the parts come from a lot of places, and I had a lot of the bits laying around already, made it seem cheaper than it really is.