Great question! I can totally understand where you are coming from. I believe you should type up your request and then seek assistance by requesting a joint meeting with your Company Commander/1SG and ask them if they would support you in obtaining your recommendation from the CG assisting you in in setting up a meeting with the Division CDR and CSM. It might not be a bad idea to ask for a recommendation from the DIV CSM as well.
The last thing you want to do is tick off the chain of command. Imagine how things will go down if the BDE CDR calls the BN CDR and says….did you know SPC X sent an email directly to the CG?