As noted by i.horsting, remove any insert packing.
I would review some of the earlier literature, and I would probably consider using a hydrocarbon solvent if others have used it ( HCs often greatly reduce unwanted junk - perhaps making splitless more of an option ).
I would seriously review your sample preparation, perhaps concentrating any extraction/extract so you're not as such trace levels.
I agree with Peter, septum purge will not remove trace material stuck to the needle, or fragments that fall into the injector. You need to eliminate the silicone in the septa - as noted above, I'd just use a different material. Your septa requirements are not to onerous.
I've always assumed that the reason I saw one nice baseline after conditioning and new injector insert and the column was because the withdrawing hot needle fried some silicone onto the surface that subsequently volatilised on the next injection.
I once carefully wiped a tapered needle outside with warm 60:40 CHCl3/MeOH after each injection, and the spurious peaks didn't appear for quite a few runs. I assumed the needle finish wasn't smooth enough to stop a fine film appearing.
I used to be a great fan of the SGE triple layered ( TCS ) septa, because that problem wasn't such an issue - compared to the instrument vendor-supplied single layer "high temperature" septa.
More recently, some of the high temperature, preconditioned and washed septa had lower backgrounds, but I'd never trust them for trace silicone analysis.
Murphy's Law tells me that a fragment of septa would somehow end up in the injector.
Once again, search out the literature, the type of analysis you are conducting will have been undertaken before.
Bruce Hamilton