It depends what you mean by 2000+ people

If you want to save humanity (but not many humans) the easier is to sent a ship with a few women and 2000+ frozen embryo. You just need to send enough people to maintain the base.  
One key reason is that you will be travelling quite close from the sun. To make a lead protection for a small fridge is no big deal. Most passengers may die of cancer a few year after arrival but they will breed sound children before that (hence the point of sending only women).  
Note this paradox: The first colonist will have no descendants. Unless some of the embryo are theirs.

The way you describe the situation: send as much resources as you can on the moon, then take needed time to send to Venus.  
The plan I describe probably allow to send a first ship before the 6 year deadline, but as o.m. suggest, send several ship is safer

By the way, a big problem in the Venus plan is: if links with earth are severed, where can you mine material to expand/maintain your floating colony?  
There is no way a few people entrapped in some balloon with few tools and no material could build shuttle and miner robot.  
If you still can access the Moon, then OK. If not, Mars is a better plan. But if the Moon is accessible, there is no real emergency to reach for Venus.