I've been bottling every batch since 1998. I can very confidently say that you definitely do NOT need to add any more yeast. If you do, you'll just have a ton of sludge on the bottom of every bottle, but no advantage from adding it.
I thought of one other concern with my above recommendation of cardboard & light bulb --- be sure to shield the bottles from the light to avoid skunking. This can be done very simply by covering the bottles with a cloth so they aren't hit by direct light.
For many, there is not a specific reason to add bottling yeast. However, I think there are specific reasons to want to add bottling yeast and it seems you don't have reason to.
I like the consistency and the control it gives me. I also want to bottle with active yeast to scavenge oxygen. In this case, the OP wants to speed up the process to hit a deadline.
It's all in how you look at it. I get very slight sediment from the amount of bottling yeast we are talking about so I can't see there be any issues with tons of sludge. In fact, it's on par with what you see in a bottle of Ommegang or your favorite Trappist ale. They are bottling in the 1-3 M/ml range and I wouldn't call what i see there "sludge" by any stretch of the imagination.
At least that's my experience. YMMV.