Here's the thing- a replica speedster is very light in the front. Everybody agrees that front discs are "de rigueur", because front brakes generally provide the bulk of stopping power on a car. However, because of the significant rear bias in most of our cars (SAS and spyders excepted), the rear brakes actually do quite a bit more of the work than we're used to.
Properly adjusted drum-brakes probably work adequately. However, they require more care and feeding than disc-brakes (which are self-adjusting). When running 4 wheel discs, a different (bigger bore) master cylinder is something that is really needed-- just putting a brake kit on, without changing the master cylinder is a recipe for middling brake performance. Some guys a lot smarter than me have figured out that the rear cylinders on most readily available brake kits are actually smaller than ideal. A biasing valve installed on the front circuit (rather than the rear) might be needed.
The take-away is that more (not less) braking power ought to be applied to the rear as our cars have a significant rear weight bias.
A good test is to lock up the brakes on a dry surface. Ideally, all 4 wheels lock up at pretty much the same time (with a slight bias to the front brakes). If you can do that with drums, then by all means-- rock on. I like discs for the ease of set-up, better "feel", and ultimately for potentially better braking performance.
Brakes are really, really cheap in the big scheme of things, especially in comparison to a stay in the ICU. A guy can do as he pleases, but I'd economize elsewhere.