My first reaction would be that despite all the goodies that could be inside, it is before all a Titan threat. Considering the danger it represents, there should an excellent reason not to blast it in pieces and shower it with EMP/plasma combo.
Greed is not enough to prevent government/corps to take immediate counter-measure. To have the spaceship avoid immediate destruction, it means that every single faction (government, corps, secret society...) with some modicum of resources would decide to hold on. Also it means that teams which would be send to explore would also need some form of guarantee that one of those faction is not going to pull the trigger wheb they are playing minecraft in the spaceship.
So I believe you need to find a good reason for people to believe it is not an immediate threat or it could be contained. It is probably severly damage, possibly large chunk of the hull did loose its protection against solar radiation which acted as intense EMP, therefore frying most/all of the exurgent threat.
Also, to had some tension, the major factions agreed not to blast it into pieces until it reaches a certain point in the solar system. It had an element of time constraint ("once it reaches coordinate omega-one, all orbital weapons will blast it including any ships leaving it). It also adds a dimension of diplomacy to build official expedition teams (but also secret one), or you can also see negociation of salvage rights for various section of the ship.
What if, contraray to your initial statement, the ship is considered "mostly free" from Titan threat as it entered the solar system, it flew through a massive ionic storm frying acting as intense EMP. The "rightful" owner of the ship (whether it is a governement, the shipyard which built it or a merc group or an insuurance company) does not want or have the resources to salvage it, but auction salvaging rights for a share of the findings ? It will give a feel similar to a gold rush.
... until, deep inside the hull, some titan monster is awaken. Or maybe it is a trap and tiny basiliks are creeping into the minds of salvagêrs and at a given time will turn everyone into the crew the ship need to accomplish its last mission: although it looks like a piece of derelict, it is fuctional, like a Deathstar.
So you can several phases:
1: Auction of salvaging rights - the players are a small independant company trying to score big but have to trade favours to get one precious salvaging license. The whole derelict battle ship is stabilised in a far orbit by additional reactors crudely fitted on its frame
2: The gold rush - the team lands, starts to explore andmine and retrieve goodies - and needs to face other teams with slightly more devious methods. Or poassibly a cult who wants to blast the whole thing. Maybe a small "bartertown" is created orbiting around the huge battleship. This phase should last for months. Unknown to everybody salvagers are getting slowly contaminated - especially after several months of exploration without incident, the teams are more laxed and control procedures are getting looser.
The reason exploration would last so long is because the whole hull is unstable and people are not supposed to bruteforce their way in.
As exploration progress, you can start to drop hints: a ship engineer could find the progress towards the system core much slower than expected... almost like the wreckage had been designed to slow down the team. Some "treasure trove" are regularly found be teams. Interestingly, after a thorough examination, those boxes or rooms had in their structure a radiation protective mesh acting like a Faraday box against EMP... some of the goodies are not what it seems.
3: The hidden monster. It is a decoy to encourage people to sent more resources. Some "minor" Titan threats are unleashed but after inflicting some casualties are neutralised. People should feel confident that they have neutralised the last remaining threat. To make it more believable, those threats where partially damaged and less effective that fully operational "monster" to support the hypothesys that the ion storm had a cleansing effect. Of course, those threat could only be found in the deepest of the hull where the likelyhood to be protected was the highest.
Again careful "autopsy" of the remains could detect that those flaws and partial damage were engineered - but it can takes several weeks for experts to reach those conclusions, delaying the warning.
It is the rush to the core. Teams are getting reinforced, working around the clock to be the first one to hit the system core and retrieve the mother payload. Caution is thrown to the window, sabotage becomes another routine activity - more people are contaminated and maybe strange dreams or behaviour are happening from time to time. At the same time, some people are getting a bit suspicious - the players because of what they have found or they are approached to investigate on behalf of suspicious people (and because PCs are on site since the beginning they will blend easily and have connections with others teams). If they are trying to raise the alarm, they will face some surprising resistance: disbelief ("you want to stop the salvaging for your own benefit because your team is behind"), or even assassination attempt from one salvager who left the field earlier (contaminated earlier). They need solid proofs as it has become a very profitable operation.
4: The race to the core. The hull seems to become more unstable, but it is a matter of day until the core system can be accessed. How careless are willing to be the salvagers to win the race ? And new teams arrived: one is planting bombs, the other has the task to stop any team to reach the core. However, no faction has yet decided to pull the trigger as the threat is not clearly identified. It is believed to be some exsurgent threat which can still be contained.
5: Deathstar in action. All contaminated men are turned into drones. Hidden machines and nano-bots start repurposing the battleship for its final mission (Luna ? Mars ?). Uncontaminated men needs to escape before getting turned into drones. Rescue mission to save an important executive or the stack of the son of an influent man - but is he contaminated ? what could do the Titan with the information kept in their brains ? Maybe it is a race to prevent a tachyon communication towards other Titan base ?
6: Destroying the Deathstar: if the cannons and other big missiles are ineffective, a suicide team has to plant the device which can neutralised definitely the battleship before it is fully functional.
One important point to keep in mind, for the Titan to escape all scanning and detection and for the trap to work, it had to keep it presence minimal and very well hidden. So until phase 5, the Titan is not aware of what is happening everywhere in the battleship, it has not spread and activated its nano-bots otherwise even the most basic scan would have trigger warning and massive strike would have followed before the Titan could reactivate any effective defense. This is important that although it is a lethal trap, because of the paranoia around titan infection and safety protocol, it is by no means omnipotent and omniscient otherwise the trap would never has a chance to work.
Phase 6 is obviously action packed - the reason the PCs are hired is because they are the one left knowing the most how to navigate into the hull. If the do not have enough fighting and destruction skills, only one or two of the are hired as guide and other players are running the core of the suicide strike team (of course their ego have been safely backed up before).
I hope it will give you food for thought.
