tl;dr -- Why not try something like the game is free for the month of October?
Seems like it's something of a chicken-egg problem. Games like this need a critical-mass to work. People stop playing because nobody else is around, which then means nobody is around and more drop, etc.
I just started playing the other day. I had played some in beta, but stopped when it went to sub cuz I was already running 3 subs in Eve and couldn't afford to do both (time and money). Dropped from Eve a while back and started to get the itch for this type of game again, so I checked it out. I saw there was no longer a monthly sub, which made me dig further. I saw that there had been recent updates and there was some forum activity, but I didn't actually read much (oops!). So I didn't realize how low the population was. What I saw (the revised EP system, etc), combined with what I remembered from my beta time, made me sign up for 2 accounts. Once in game I noticed that nobody was around. After reading the forum and watching GC I had the same thoughts as the OP. If there were some mechanism to let people have something like 21-30 days free time as a big event, it might be enough to boost population up for a couple weeks and get new players to actually pay and get invested. Implementing a free trial for people as they trickle in probably won't work. You have to do something to get a spike.
I wouldn't even put any restrictions on the gameplay. Treat everyone during the event as if they were full paying customers. That way they see what it is really like. Could it be exploited? Maybe. Would it be "FAIR" to current players? Not completely. But what is better for current players - a dead game or new active blood?
When the active population hovers around 75-ish it is going to be tough to have much fun. I am so far having fun just doing the solo starter PVE stuff, re-learning the skill system, fittings, etc. But I ultimately would want to get into pvp. That was my thing in Eve (the cloaky w-space kind, lol). I'm not seeing much potential for that right now.
My thought is -- what do they have to lose? It's hard to recommend that my online gamer friends plunk down even $10 to play an MMO with 75 people. When I dropped out of Eve I went the opposite direction and checked out LOTRO, largely because it was free to start. Once I played for a few weeks I ended up dropping money on the expansions and subscription. I've spent about $250 over the 18 months. That would not have happened if I had to start by paying money.