I was under the impression a BCD voided most VA Benefits but not all.
Did you try getting the BCD changed to OTH?
The following was taken from another thread here on AMHD:
Eligibility for most VA benefits is based upon discharge from active military service under other than dishonorable conditions. Dishonorable and bad-conduct discharges issued by general courts-martial bar VA benefits. Veterans in prison and parolees may be eligible for certain VA benefits.
Bad conduct, dishonorable, less than honorable or undesirable military discharges which may prevent eligibility for VA medical care, pensions, compensation or other benefits can be changed by applying to the appropriate military service's discharge review board. To learn more, see: US Military Information
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When you say the Marine Corps. Who specifically are you referring to? When you say the Marine Corps. You are implying whomever you spoke with shares the exact views, beliefs, knowledge and opinions of the entire Marine Corps. Which is innaccurate. Refer to Billet, Rank, Name etc... NOT the entire USMC! (unless of course you have spoken with Gen. Amos/Commandant of the Marine Corps)