Your starter clutch is on its way out, as is often the case with these bikes. You can rebuild it with these (need 3 of each)

Genuine Honda - Starter Clutch Spring - 28125-253-020 - CB160 CB175 CB350 CB360 CB400F
Genuine Honda - Starter Clutch Cap - 28126-253-030 - CB160 CB175 CB350 CB360 CB400F
Genuine Honda - Starter Clutch Roller - 91101-377-000 - CB72 CB77 CB400F CB450 CB550 CL450 CB500T

or

CA72 CA77 CB72 CB77 CB350 CB360 Starter Clutch Repair Kit 91101-377-000A | Motorcycle Solutions LLC

 

Makes sense. It wasn't in the best shape when I had the motor apart. Can you give any insight on why it only happens when I pull the throttle?

 

It does sound like starter clutch, and the likely reason it's worse when you turn the throttle is because you're adding the load on the starter of bringing in more volume of air/fuel mix into the combustion chambers when you do. It's a simple enough job, just the alternator and front sprocket covers need to come off (you'll lose some oil when you take the alternator cover off) and then you'll need a rotor puller (and if you have a 350 rear axle available, pretty sure it's the same size and thread). There are 3 big JIS Phillips-type screws on the back of the rotor to remove the outer clutch starter housing to replace the pieces, as long as the housing isn't cracked. When you re-assemble everything, make sure you either use Loctite on the threads of those 3 screws holding it together or "stake" them into the slots on the outside edge of the screw holes to help keep them from backing out in the future

 

Unfortunately, one of the screws is shattered. I'll have to hit the machine shop. I'm just happy the engine started back up after the rebuild.

 

Makes even more sense to hear that - the entire assembly was shifting and not gripping well at all under max load. Hopefully the machine shop will get the screw out - be sure they understand to be careful with the rotor, if it gets hit hard during their efforts (or dropped) it could have an effect on its magnetism strength