I'm answering this frankly, as unfamiliar with the referenced model, but not wishing to see Forum questions going unanswered. My first question of what exactly an SDT abbreviation represents, a quick Google produced the following from a Gunbroker listing reflecting recently "Sold"; perhaps yours?
"JM-stamped Marlin 336SDT "Stainless Davidson's Trapper" chambered in .30-30 Winchester with a 16" barrel and fiber optic front and rear sights. Rifle is from a limited run of 501 rifles made for Davidson's by Marlin. Rifle is in excellent condition with some slight scratching in the finish from the safe. Bore is bright and shiny. Wood is excellent. No box or papers."
Noting sold price as asked $3K!" Such Gunbroker closed listing.
Second question as the source of your "...very desirable collectible" determination? Such as a 'usual suspect'!
Stories as propositions alleging enhanced value attaching... Giving rise to the fundamental gun buying proposition. "Buy the gun, not the story!" The best, 'safest approach'. My system, consonant. As as being drawn to a gun for the physical gun itself. Stories, even IF true, at best accorded 'nice to know' as perhaps someone else impressed. Myself, never a pure speculator! Paying only a price compatible with the guns 'worth to me'! Beyond, as walking! Saying that, only other consideration, as combo of 'the hots for it' and likelihood of finding another similar specimen in consideration of my time and efforts. Some personal premium perhaps accrued in my offer as well as convenient self-excuse for 'small premium'.
Your particular rifle, IF I were interested, my considerations in valuing to self. First, red flag, whether "Remington parenting Marlin" production era! Stories I'd be more likely to buy, dissatisfied owners reporting problems surrounding poor quality; aesthetics and function! Of Warranties gone with Remington Bankruptcy. Second, some necessary 'value added' eura. Yet distinguishing as accord long established for such as "Commemoratives', usually reflected objectively in superior wood and finish as well as material component differences; barrel lengths configurations; engraving; etc. Conversely, 'Jobber specials' reflecting differing sights and wood finished from regular production; more as rearranging Titanic deck chairs touting 'worthy collector differences'. The "package I see, unimpressive and absent perhaps some sort of unique "tool room", 'one off', with provenance; seeming unimpressive.
Now! All that said, we are in an amazing era. Housing bubble, maybe just receding. Gun value 'bubble' aura of "regulatory controls worries; "get 'em while you kin". So "value as especially reflecting venues of national buying audiences; wild. I can't estimate the value of your rifle in "current" perspective. In 'historical' perspective, the remark that the guns which increase in sales price fastest, reflective of "artificial inflation", tend to fall fastest. Those accruing value over decades, generally holding much better as established collector audience.
My net. If you're in love with the gun, congratulations. If you're in it for speculation, condolences!
Either situation, wishing you "Best!"
John