Sistering a damaged joist with 2 smaller pieces of wood
You've asked whether it's possible to get the repair joists in place. We can't really know that. The plan is reasonable, though. The key is to make the sistered joists long enough (or long as possible with adequate fastening). The shorter they are the more torque (shear) is applied to your fasteners and the wood fibers. Ideally you have a 4:1 lap-to-span ratio or better. 

The block in the center isn't really necessary. It won't do anything of value. Install the other two and secure them to the original joist with construction (not black drywall) screws, or through-bolts, and heavy-duty construction adhesive. 

Since it's just one joist that needs repair, it's not critical that you meet sky-high standards for load bearing. If you approximate the strength of the original joist the repair will be adequate. Good luck.