The thing is that his sister and brother are living at Moddey. So he really should be able to see them sometimes, right? Even if it's in safe houses.

If he wants to see them, then he should get to now and then. Somehow.

That doesn't necessarily mean he needs to be admitted into the Order (and doing it today would have been mad, you've no way to know if he'd just go tell the Crimson Company he met Sirius!) but maybe he could help us the way that Ms Taylor sometimes helps? Just by telling us things now and then?