Glad you found out some more info about your grandfather. Not sure what you want to know though. This question isn't very explicit.
Here's the deal based on the sequence of battle action that you listed in your question. I suspect your 1st guess of the 3rd Marine Defense Bn was likely correct.
1st: The 3rd Marine Defense Bn was providing air defense in Hawaii when Pearl Harbor was attacked by the Japanese December 7, 1941.
2d: Not much later, there was a detachment of the 3rd Marine Defense Bn assigned to Midway Island to defend it against a Japanese invasion. They were relieved by the 6th Marine Defense Bn and likely rejoined their main Bn in Hawaii.
3d: The 3rd Defense Bn participated in the battle for Guadalcanal as part of the 1st Marine Division. So far, your grandpa is 3 for 4 locations if assigned to the 3rd Marine Defense Bn.
4th: This is where there is a change. Bougainville was fought by the 3D Marine Regiment. The 3D Marines did have a 3rd Bn as did/do all Marine Corps Regiments. What is likely to have happened is that as the Guadalcanal battle wound down, the Marines on the island were reconstituted (reorganized) into new battalions that would be needed for defense of Bougainville. He could have been re-assigned to the 5th Marine Regiment and transferred as a member of that unit. Bougainville was a series of defensive battles that lasted from 1943 thru 1945.
His "injuries" could have been wounds suffered during the defensive/offensive action or he could have been injuried in the process of doing his duties. The injury/wounds resulted in his being medically evacuated to the US.
I did little more review of the defense battalions. They were essentially Marine artillery and air defense units during WWII. They were responsible for repelling enemy forces from land and air approaches. Their organic weapons consisted of 155mm and 90mm artillery (big guns), 40mm, 20mm, and machine gun anti-air weapons to shoot down enemy aircraft. Considering this, it would make sense for the Marine Corps to move his Bn or a new Bn that he may be attached to from Guadalcanal to Bougainville to beef up its defense since the Japanese wanted the islands air strip - they lost the one on Guadalcanal.
You didn't say what country you live. I still recommend submitting SF86 from the National Archives site (www.archives.gov), complete the form, and mail it to them. If you have access to an FPO or APO (military member), they will respond to that address. If you do not, recommend have the records sent to a family member or friend in the US by using their address on your form. They can forward the info to you. The VA is a useless approach though a few people profess they had success. You don't have to go through a middleman for the records as next of kin. You can go direct. Neither the VA or govt will send mail to foreign addresses due to the expense - APOs and FPOs are an exception - the postal rates are same as US postal rates with no foreign postal system involved.
Best Wishes. You need to make any future questions more explicit as to what info you want. Above is my best guess as to what you are looking for.
Lieutenant Colonel, US Marine Corps-Retired
PS: You can also google some Marine Corps history by using terms such as "3rd Marines WWII".
EDIT: Puma is only partially correct. The web site is as I noted above. The address is St. Louis, MO not the National Archives located in MD. MD is the place that the Federal govt, including the military Services, ship their non-personnel historical files for permanent storage. All personnel files are sent to St. Louis.
During a tour at Headquarters Marine Corps, I was responsible for sending Marine Aviation related files to the National Archives in MD. All Marine and Navy files are sent to St. Louis, MO. There is a branch of the Navy Dept located at St. Louis who provide the interface for transferring personnel files into the National Archives military personnel file data base. All WWII, Korea, and Vietnam War era files are mostly in paper format. Some have been put on mirofishe (mine were converted to microfishe in 1984 since I was still on active duty. Those personnel files for those not on active duty remained in paper form.
The St. Louis personnel record archives will send you a paper copy of your grandfather's files. The website tells you exactly where to send your SF86 form - St. Louis, MO. Once you receive the records, you will be told to submit a specific request to the Dept of the Navy Personnel Branch, St. Louis, MO to request an issue of his medals and ribbons (you will only receive those that are US issued, no foreign awards).
LtCol, US Marine Corps-Retired