As a native English speaker, I think that Russian spelling is wonderfully, blessedly, beautifully logical!

Perhaps the only thing I would change is to replace щ with a completely different letter that does not resemble ш -- maybe using $ or ç, for example. So щи да каша пища наша would instead be spelled $и да каша пи$а наша or çи да каша пиçа наша. This would make it easier for me, as a foreigner, to remember when to use the hard "sh" and when to use the soft "shch".

Apart from that, I don't think I'd change anything.