As was said already, we don't have all the necessary data to give you a good answer. but we can do better than cathay.
your goal is to arrive at the destination with maximum fuel remaining.
we've traditionally used LRC speed as the most efficient cruise speed, but this is only true with no wind. btw LRC speed itself does not change with wind.
LRC is not useful for your purpose in wind because its goal is to maximize range. our range is fixed, we want to minimize fuel consumption instead.
Here are some generic charts to help the discussion:
as was said before, fuel is not the only cost, time is also a cost. not only in that we have to maintain a schedule (let's say that's not relevant to this question) but also in that the longer the trip takes, the more fuel used... so time is fuel, and there is a balance point where going any slower will COST fuel rather than SAVE fuel:
wind does not affect TAS or mach. if you want to take wind into consideration, shift the mach number in the two charts at the top (7.8 and 7.9 - headwind=lower resulting mach, tailwind=higher) and the result will be that in the bottom chart(7.10), optimal mach number changes very little! what changes is that the whole banana shaped curve moves down to a lower cost for a tailwind, and up for a headwind. These are typical numbers for a 757 (couldn't find an RJ one, but the point is that the change is very small)
so how do you make this useful? for academic purposes, no change is required, or you can change by .1 mach for 100kts of wind... for real world purposes, schedule does matter, so my technique is (probably the same as everyone else's...) to increase in a headwind with fuel remaining as a guideline for how fast to go, and to decrease in a tailwind, with ETA as a guide but no less than LRC TAS. if you go slower than LRC, you're wasting gas.
the cathay trick is probably a general rule of thumb for aircraft without FMS. I can't think of a reason to use it, if you have a fuel remaining and ETA estimates that allows you to adjust your speed to exactly what you need. if you have enough gas, the adjustment will be the FULL wind value, not half. and if you were filed close to LRC, you wouldn't decrease by half the wind to a value below LRC.
AERO - Fuel Conservation Strategies: Cruise Flight