I don't think the Detroit private schools have those trips on their schedule. Not that I recall. Toledo is not a trade-off with out of the Metro private schools for them. Would they trade-off closer games against Stevenson and other outer belt publics to fill Toledo's needs? Don't know.
I know UDJ has played EGR a few times in the past few years, and DCC and DLSC have both played Musky in the last half decade during the regular season, and Brother Rice goes all over the place, but they absolutely have enough Metro Detroit teams to fill which would be far easier. Theyre just the closest who would likely have the ability and/or desire to do so given their larger non-conference slates.
DCC has a now long-standing series with Whitmer (7 years I think, and it doesn't appear either is running to end it), so they are open to doing in, and MLK has played TCC in the past. UDJ may see an interesting connection with SJJ, and DLSC and SFS are both Franciscan, so it's not COMPLETELY out of the ordinary...but you're right about it still not being a sure thing.