There might be prudent reasons for forming the LLC but I don’t think it’ll help you with financial aid.
You’ll still need to report the asset, it’ll just be reported as part of the business value rather than a personal investment. There’s a question on the FAFSA where you report business value. For schools using the CSS profile, there’s a business supplement that you’d fill out for each business which asks pretty detailed questions about business assets, expenses, etc. Most schools will want your 1120s for the S Corp (and yes, they’ll ask you to place a value on it) and probably the 1065 if you file that for the partnership. Your wife’s info will be on the schedule C but they’ll ask you the value of that business also.
So there’s really no hiding any assets in businesses. You’d be better off from a FA perspective with that equity in your primary home (at schools that don’t consider equity in primary home) or better yet in an IRA/401k.