ME, that's who.
It's true. With absolutely no help from anyone who knows anything about hackers (thanks to the horrible tech support staff provided by our host services), I found the offensive htm file and got rid of it.
(I hope that's all I needed to do.)
And now our homepage is working just fine.
To celebrate, here's a code you can use to get 40% off your next order: GENIUSme
Also, you can send me congratulatory wishes for being such a tremendous genius in the form of chocolate and a nap.