The front half of my ground floor, on which I'll be installing hardwood, has joists running back to front. The back half has joists running side to side. The subfloor is 3/8 particleboard, which I cannot remove as I have previously screwed drywall to the underside of the subfloor, for sound-deadening purposes between the basement and ground floor.

I understand that laying the hardwood parallel to the joists is a bad idea. It would seem my two options are to change the direction of the flooring in the back half, or lay the flooring diagonally.

Are there any other options that would make it possible for me to accomplish laying the flooring front to back throughout the entire floor?

Oops, I got the joist direction wrong: joists are side to side in the front, which means I can lay the flooring front to back there, but it would end up parallel to the back joists, which run front to back.

Your sub floor is too thin for hardwood. You're sure it's 3/8"? What is the distance between the joists?

What JIMMIEM said. The 3/8ths is kinda scary. Who would use 3/8 for a subfloor. I doubt thats even code.You need another layer of 3/4 inch plywood. Then you can run it anyway you want.

Sorry, more incorrect info - the subfloor is 5/8 OSB

5/8ths sub-floor is the minimum. I would recommend a full trowel glue down of ¾ inch flooring. You can also use nails, cleats or staples to hold the flooring as the floor is laid. Gluing the flooring to the OSB will ad a lot of strength, making your floor over an inch thick. Be sure to fasten the sub-floor well before you start on the finish floor,8d nails every 8 inches, minimum. If nailed by hand you will know if you hit a floor joist.