So Yonah’s got a post up where he’s like “damn, this transfer station design sucks, but, I guess there’s nothing better we can do.”
Seriously, bay platforms. LRT is POP so there’s no fare control issue, since the TVMs are already on the platform anyway. This is so simple that you don’t even need a decent graphics program to explain it. Here it is, freehanded in MSPaint.

Average transfer walk distance is less than a trainlength. Wide platforms let you put escalators in the center and elevators at the ends, which makes for a coherent space.
I know some transit terminology, but for those less informed, could you explain what is meant by POP and AGT? So I don’t have to decipher various possibilities from acronym websites?
POP = “Proof of Payment,” a system where you have to buy a ticket and then fare inspectors may or may not be on that particular train checking your tickets. Houston METROrail works this way, as do most other newer light rail systems.
AGT = “Automated Guideway Transit.” This is basically anything without a driver, but in the US we’re oldschool, so AGT is roughly synonymous with “airport people mover.” A lot of the original airport people movers back in the 60′s and 70′s were installed by Westinghouse, who also wanted to build a comprehensive system in Pittsburgh. Alas, ’twas not to be.
The RFP for the Crenshaw Design/Build is already on the street (I forget if the deadline has passed yet or not), so unfortunately in this particular case, the crappy transfer may be a foregone conclusion. I say may, because the people mover is a little further out in the future, so maybe something can be done with that design.
I’m not quite sure why people are so fixated on getting a direct rail link to LAX, and more specifically, between LAX and downtown. If you want to get between LAX and downtown, the Fly Away bus is far and away the best option. It makes use of HOV lanes on the 110 and the 105, which pretty much ensures that LRT is never going to compete for travel time.
Beyond that, downtown LA is a relatively minor factor when you’re talking about the region. I think there’s a tendency for people to want a connection like Boston or Chicago, but LA’s polycentric nature reduces the value. If you’re going to the Westside/UCLA, or Burbank, or Long Beach, it doesn’t do anything for you.
A rail stop closer to LAX would be nice, but it could be addressed through a transit line that more or less parallels the 405 between the SF Valley and Long Beach (you could have a stop at Sepulveda and Century). That would put a stop closer to the airport, create a ton of value in its own right, and greatly improve the utility of the rest of the rail system.