I can accept that. Makes sense given the long-range nature of the E's mission. A backup power plant in each nacelle is a logical development given the imagined state of technology.
Smaller backup reactors make sense as well, they don't have to be that big, maybe foot-locker sized... just for generating power to the ships systems and providing that needed "kick" to get the matter-antimatter system up and running.
Now that I think of it, the cold-start issues could stem from waking up the nacelle reactors, you'd have to arm the system, boot the computers, establish a handshake and begin making plasma, prepare the antimatter and establish an intermix ratio and balance the injection sequence before applying power to the coils. Attempting to bypass all that leads to all sorts of freaky shit happening like short time hops and whatnot.