There's a flaw in the idea. If you give the contestant an item for free it may end up being the item that goes in the mailbox. In that case you'd be giving the contestant $1,000 without having to price anything.
No matter what you pick it doesn't make the game any easier. You still need to place the other items if you're playing to win it all. If you got one of the items for the middle levels as your free choice it'd still be tough figuring out what goes with it. Getting the top item is basically a wasted pick.
Also, there's no guarantee that there is only one solution per playing, so it might not be possible to give a free guess. Every recap I've read here has shown only one solution but we can't be sure it's set up like that every time. If so, maybe the fact that there is only one solution is something the show does not want to reveal. Giving them a free pick would give that secret about the game away. Just because LFaTs and the producers know there's been one exact order per playing thus far doesn't mean the contestant should know it.
I'd say just lower the top prize and then change the types of grocery items. Why does the top prize have to be $100,000? If the top prize was $20K it'd still be a good amount to go home with. With the top prize lowered they can then afford to make the game easier by using grocery items that vary more in price. Making this game more winnable and easier to play along at home will make it better TV.
Slightly OT but if I were advising a contestant about playing Pay the Rent I'd suggest thinking about it top down. Even though Drew has you place the items from the bottom up if you thought about what should go up top first (i.e. identifying the most expensive item) then work your way down it'd be an easier approach to the game. Not that Drew should have contestants place them top down but the contestant should keep mental notes on it.