Having a robust OMS system is essential to SSAs capsules for a couple of reasons. First, it serves as a reusable upper stage. It's not just a workaround for the pitiful booster. Having your engine return saves money, and is a part of the value proposition for an RLV. Second, for the jobs Mangussen is likely to do (satellite repair), significant orbital maneuvering may be needed.

Due to the small size of Mangussen, seats cannot be re-oriented (like on t/Space's design), or even reclined (like on Shuttle). Therefore, the thrust of OMS has to point in the same direction as deceleration for landing. Such geometry mandates OMS going through the heat shield.

I mentioned this problem on some other blog before. The biggest risk Rocket Girls face in this area is the door malfunction. If doors fail to close completely, crew gets roasted, like the crew of Columbia. Unfortunately, this is not an impossible scenario... Especially if we remember how a floating plastic bag obstructed a docking port on Mir. Tanpopo left the engine extended for the duration of the mission, which only increases chances of such things happening.

Meanwhile, in the real world, holes in the heat shield are not entirely unknown. Shuttle has doors for feedlines from External Tank to main engines. Russian TKS had a crew access hatch in its heat shield. The difference with the likes of Tanpopo is how the closing operation can be recycled with human intervention if required.

To summarize, the design used in Rocket Girls is not implausible, and is the most direct, even naive approach to solve the problem. It just takes stupendous risks, that's all.

{P.S. Dragon avoids the issue by using fairly wimpy OMS. It thrusts backwards, so astronauts have to hang in their harnesses for a few minutes during the deorbit burn. Back of the envelope calculations suggest about 0.15G for 5 minutes: certainly not insurmountable. At worst some wimp might need to hold his head with his hands a bit.}