How can I get my security clearance adjudicated more quickly?

You are making a joke??? The subject of an investigation is wanting to do his own adjudication???? If I rob a bank, let me do the analysis of the information...and I will not go to jail. DCAF does all DoD adjudications. CCF is long gone, but mostly folded into DCAF. The first Senior Executive (SES) was former Army commander of CCF. Those professionals will do the adudacations. They are a little busy. You can wait. Others with more important jobs have a higher priority. (Like a linguist with three hard languages...yes, they are more valuable than you and I.)

Unfortunately, this is not something anyone other than your security manager (or someone above him in the chain) can "fix".

When you get to a unit, part of your inprocessing is inprocessing the S2. The S2 then processes you in JPAS (the big security clearance database in the sky) and "owns" you. There is a secuity chain, similar to the chain of Command, and if you are "owned" by BN, you will be owned by BDE, DIV, etc. So higher echelons can play with your file, but other echelons cannot. You can't walk to the BN next door and ask their security manager to help you.

All that being said, the unit security manager is not who adjudicates. Likely a delay in adjudication is a backlog at OPM - which no one outside of OPM can really help you out with, short of a high level Commander (like birds at a minimum, more likely stars) calling and saying you need to be expedited for time-sensitive mission-critical reasons. I am guessing that is not the case, so you probably just have to wait for OPM to finalize the process.

I know that is not what you wanted to hear, but based on my experience working the security clearance desk and the little info you provided, that is the only solution I can see.

An age old problem that seemingly is impossible to resolve. They had a big push in the 60s on all pilots having at least a TS. Progress was announced weekly with few changes. Our executive officer was one of those who dragged on and on. HQMC finally ran a check on it and it turned out his mother-in-law was a member of the NAZI party during WWII in Germany and they were having trouble doing all the investigating.
Sit back, smile and have faith, this too shall pass!