Tricks for getting short 3mm cover screws to go in completely?

I am a computer consultant and I have replaced memory on many unibody MacBook Pros. I am very familiar with the cover screws and always use the correct #00 Philips, etc. I just purchased a "new" Mid-2012 MacBook Pro, so it's been sitting on the shelf since they were discontinued last fall, at least.

Anyway, upon its arrival, I immediately opened it to put a larger hard drive in it. When I closed it, I had trouble getting three of the cover screws on the short sides of the computer to screw back in properly. I notice they had thread lock on them from the factory. I think it's blue Loctite. I am wondering if it would be smart for me to clean this off (Loctite specifies a pretty nasty solvent for this) and put fresh blue Loctite on, if I'll have a better shot at getting them to go in properly. The other thing that makes these screws tricky is it's not really clear what the angle of the hole is, as the surface of the cover is crowned/sloped right at the entrance. Is the hole vertical or is it perpendicular to the slope? One is not sure which direction to apply force with the screwdriver when starting the screw. It's easy to accidentally cross thread these for this reason, although I must say, I've been successful many times. This is the first time I've been this stumped. Plus, it's brand new computer, and I want it to be perfect. Any body have a trick for nailing these every time? Am I all wet in blaming the thread locker? Do hardware specialists freshen the thread lock with every disassembly-reassembly?