Well, you have the reason why the crew is undertaking the voyage (delivering blueprints) and that they are trying to set up some sort of food manufacturer at their destination (or that they are transporting the final component, whatever catches your eye).
An idea for why the crew is all female could be for weight management, that having several men onboard may compromise the integrity of the ship (in conjunction with the rest of the heavy equipment), having females would be a cost-effective way to not have so much food rations on board while also giving them tech to do just about everything more than any men could do (like that power loader Ripley used in Aliens, maybe something that only females can use). The question is how many; by going by the idea you have you’d need a captain, engineer, scientist, a worker or two, and a medic at least for the ship and crew to function, so how many are involved is up to you.
A reason why they don’t use cryosleep or hyperspace could a few reasons. Hyperspace in Star Wars, despite them not showing it, is a very dangerous form of travel. One wrong move and the whole ship could be ripped in half, or if the hyperspace isn’t shut off in time you could ram into a star or planet (resulting in a massive explosion which could wipe a whole system), lastly there are things that exist in hyperspace that are nearly unkillable, so plenty to pull from here as to why tech like this isn’t implemented. Cryosleep, and by extension hyperspace if need be, could be that tech isn’t that far along to allow for such ease, the crew has to stay awake and maintain the ship until they reach their destination. In a way, this can allow for the ship to have plenty of things to do since there will be a ton of downtime, just to kill the boredom until the mission is complete. If none of these work for you, maybe go for the ship is traveling to Europa (Jupiter moon) so none are required to reach it. Still, that would leave a ton of downtime that would require facilities to pass the time.
The protag joining could be to fill one of the jobs I listed in the crew section, or that they have their own particular job only they can do, like maybe the ship’s mechanic. This would make the character vital to the mission’s success (since they keep the ship running) but can allow for some scenes once the weight begins to pile on (fighting with their breasts getting into vents, belly and hips getting wedged in a panel opening, etc.) Not to mention they would have decent physicality that can handle higher weight levels.
For why they are gaining weight, if we go with the Europa idea maybe as they pass through the asteroid field (or take an unusual way through it instead of the normal routes) that the ship is hit with an asteroid and a fungus gets on board. The fungus requires fat to survive so it influences the crew to slowly fatten up as it gains power, even using the food synthesizer to speed up the gain.
Just a few ideas here, maybe they could help. The concept sounds good and I hope its well made.