Is the 1" subfloor actually 1" plywood or something else? What is the exact thickness?
Is gluing and bolting/nailing a board sufficient to support the floor?
Yes that's fine. It doesn't even have to be 2x10. 2x8 or even 2x6 will work if it helps avoiding obstacles.
However it looks like you'd have a tuff time installing blocking between the joists where new ply meets old. So, you'll probably have to install new multiple sheets to equal the old, then install an underlayment of min. 3/8" to overlap all seams. This is a must cuz you do not have the t&g anymore, good idea anyway.