Razor, may I suggest to you on obtaining a copy of the US Army Marksmanship Guide. The proper use of a leather sling and shooting glove will help your offhand marksmanship a great deal. Wooble area will decrease and sitting position will keep them rounds in the black.
With practice guaranteed. Those items I spoke of will enhance your scores and enjoyment of the sport.
BTW, You don't need the buttstock sling attachment when using a US Army Model 1906 Leather Sling as it will be wrapped around your left arm if used by the book.
;) Paul