Taking on pilgrims to make money would be an excellent way to make money. Terra is (unsurprisingly) a major religious site, although you probably want to avoid the extra time to make the full tour along Ophelia, Chiros and Gathalamor. Perhaps you could even pick up a few Sororitas novices scheduled to take their vows in the Ecclesiarchal Palace. All of this nets you a chance to score some points with the clergy of the Imperial Cult, which in turn could potentially pull a few strings to ease passage into Sol. After all, agents of the Ministorum can be found on every single capital ship of the Navy and in almost every greater noble's household, the Ecclesiarchy has a seat in the Senatorum, and lastly, all those other pilgrim vessels normally travelling to Terra would face the same means of scrutiny as you would.
Another idea, perhaps in addition to the above, would be to import exotic goods to trade, ranging from precious minerals to livestock to true collector items such as various tokens of local manufacture from half across the galaxy. Depending on the monetary situation, the players could sell it en-route or even try holding out until they reach their final destination to make one big sale - with the tricky thing being that they already need something to barter whilst being en route, yet the further they get away from the original starting point of their journey, the more valuable the stuff in their cargo hold becomes (potentially).
These two suggestions also include interesting hooks for the difficulties you mentioned, though. For example, taking on so many pilgrims from different worlds could result in unrest between multiple groups, considering that worship of the Emperor, albeit Ministorum-guided, is usually a very local matter, differing in rites and practices from world to world. Although the Preachers themselves should be instructed regarding the Ecclesiarchy's policies in this matter, the worshipers themselves could very well regard each other as "heretics" and, in the worst possible situation, attempt to wage a holy war right in the bowels of your ship. Needless to say, this could also negatively impact any relationship you might attempt to forge with the Ecclesiarchy at large.
If the players already have some experience with transporting passengers, they might manage to alleviate this issue somewhat, especially if they think of segregating the people somewhat based on what planet they're from. If the command crew includes a cleric (player or NPC), he or she might advise them of such potential troubles and maybe even offer to coordinate things; an excellent opportunity for a player Missionary to play their role!
Another difficulty with passengers, at least if the players wish to maximise their income and try to get some very rich people as pilgrims, is that people could start making demands regarding their accomodations. The various nobles would probably be used to be treated like kings on their respective planets, but when you have hundreds or even thousands of them jammed together in a shoddy cargo hold, then things should get interesting. Ongoing or long-suppressed feuds being brought up, new ones being made, obnoxious arrogance directed at the players … in many cases, it would be a similar, yet totally different situation than just having to deal with poor pilgrims, for although there might be an obvious hint of antagonism in the air, any incidents would revolve not around huge fist-fights but rather political scheming, backstabbing and duels with pistols and sabers. This here might be the territory of a good Seneschal.
Lastly, the import of exotic goods could throw up possible issues with Imperial customs policies, or whatever the IoM has in place regarding interstellar trade. Animals being regarded as a threat to people's health, the local ecosystem or even just spiritual purity, any artifacts coming under scrutiny for "xenos taint", et cetera.
And then there would be the uncertainties of travelling an entirely unknown/unestablished trade route, for when visiting various worlds along the way, the players may very well find that some items in their cargo hold are worth only marginally more or, in some cases, even much less than the price they have paid to originally acquire them!
There's some more potential for good roleplaying and dice rolls in this one as well, for careful investigation and chit-chat with fellow traders or Imperial officials could confer some knowledge of what to expect in the next star system.
On a sidenote, is the Rogue Trader aware of the dangers that could await him on Terra? I'm going to assume that you wouldn't "lock down" or even kill the player's character, even though this risk would exist within the setting - depending on the Trader's psychic skill and willpower. The Inquisitor could very well be biased, regarding it as her duty to nudge anyone to take the tests. But if the Rogue Trader himself does not know a lot about stuff like the evaluation, training, soulbinding and the sacrifice, perhaps you could intersperse a few rumours that the crew picks up along the journey, making for uncertainties and doubt come up right when the ship is already underway, the Rogue Trader getting more nervous the closer he gets to Terra…