I have not yet given birth (31 weeks and counting) and totally understand your anxiety about a late change to your plan, especially given your sister's experience.
But I thought I would offer a contrary view - many people would feel lucky to have their risk 'downgraded' to MLU level. MLUs offer a gentler environment than consultant-led wards, women are supported in a more holistic way and there are options that in some cases do not exist on a CLU, eg water pools etc as a form of pain relief.
You're also statistically less likely to have any interventions (partly because you're low risk and partly because, as I understand it, women are often given more time before interventions are encouraged) and you may have better access to breastfeeding support and also better visiting hours.
If the MLU is attached to the hospital you are in a win-win situation, a lot of excellent opportunities to have these options, with full back-up and more medical pain relief available nearby if you need it.
Some people will never have that opportunity - due to complications or BMI or the fact that there simply is not a MLU facility available (like in my area - I have CLU or homebirth options only as they recently closed the FMU).
Why not ask someone how long it would take to be transferred and have an epidural sited? However, if you really really want to close the door on the MLU option, then you should be able to request it.