Carbon dosing and stirring up the sand bed?

I'm trying to get my sky-high nitrates down. It's slow going and kind of frustrating. I am going to try carbon dosing (vodka method) for the first time to try and get the NO3 down a bit quicker. From everything I'm reading, C dosing seems to be pretty effective and has several benefits in addition to lower N and P (e.g. improved water clarity, improved coral coloration, etc.).

I have a question about my sand bed with regards to C dosing. My nearly 10yo reef tank has the same fine, oolitic aragonite sandbed I originally set it up with. Obviously, in 10 years, this sandbed has probably accumulated/trapped a fair amount of detritus.

I know the general consensus is that if you haven't been in the habit of regularly stirring and/or vacuuming your sandbed, you should not suddenly start doing so. I'm wondering if C dosing changes that at all? If I start C dosing, will I be able to start stirring up my sandbed a little bit at a time in order to let the bacterial bloom from the C dosing get at the detritus? Will the increased bacteria help reduce the detritus/nutrients with which my sandbed has become clogged? If so, can I just stir up a small area every 3-4 days or so and let the C dosing bacteria consume that and be exported via skimming?

I love the look of the sandbed in a reef tank, which is why I've kept it in my tank all this time. However, if I was starting all over, I'd probably go bare bottom to avoid this detritus sink issue. Unfortunately, taking out the sand is not an option at this point. So, I need to find a way to clean the detritus/nitrates out of my sand without causing a total system collapse.