I think the main issue here (and this really isn't intended as a dig) is most people are buying these cars because they drive well - fitting stretched tyres and massive camber to accommodate a nice set of alloys is going to compromise the drive, so it's not really within the 'sphere of experience' of most on this forum.
To be quite honest, looking at the poke on those alloys, and having run the numbers vs OE alloys on willtheyfit, I'd say you would definitely need Coilovers and lower camber arms to get those rears to fit, and probably quite a stretch on the tyres!
Could always look at getting hold of some M Front and rear suspension - the hubs are at different offsets more suited to wider wheels, and although relatively aggressive, you would be able to run 9J fronts 10j rears without any real problems (I run 10J rears without camber mods and quite aggressive tyre sizes on my M). From what I've read, on the M you do need to be running fairly aggressive camber (~3degrees or so) on the front to accommodate a 9J. I really can't imagine the Si would accommodate it without removing the arch liners completely, and running a silly amount of camber.... 10J Rears looks......ambitious!!!
EDIT: It actually looks like the biggest issue is the current offset of the alloys - have you considered milling the centres down a bit to reduce the poke? Looks like you have some room against the specs of the original alloys - the rim of the new alloys will be aprrox. 9mm further away from the suspension strut at the rear? I've never done this before so don't know what would be involved, or how much metal would be safe to remove from the centrebore, but worth a look into surely?
https://www.zpost.com/forums/showthread.php?t=506796
Looks like this guy above managed to get 19" 10J alloys to fit the rear, and 8.5J Fronts and he mentions they rub like hell (see quoted extract below) - but looking at the offsets they're much more favourable to working with the 3.0si...!
Wheels: Linea Corse LC818
8.5x19 and 10x19
Offset is modified from ET30 to ET34 (F) and from ET37 to ET40 (R).
They are really for BMW E9x.
Tires are Michelin Pilot Super Sport 235/35 and 265/30
Havent heard any rubbing from the rear, but it rubs like hell in the front. Have to do something with the inner plastic thingies.
Suspension is H&R 35mm springs with OEM M-Tech shocks.
Sorry, appreciate all this is off on a tangent to your 'is this legal' question, but hopefully a bit helpful?!

:idunno: