If you had to order a home button off ebay anyways ($5), my suggestion is get the replacement screen with home button installed ($20). The home button seems secured by plastic pins melted by a press. You'd need to mimic this with an iron to install a replacement, if there was enough plastic left, or a precise hot glue gun maybe. Too much heat would kill the button, not worth the $15 to try it in my books.

Good luck, looks like the original was set onto plastic pins that were then heated with press. You'd probably need to remelt the plastic pins with the home button pressed firmly in. When you order your replacement screens, always pay the extra $5 to get one with the home button included. Good luck