"Collector" is a description,not a qualification. And the "collector" who advised you does not appear to be an expert, but is in fact disqualified as such by the statement that a 1915 DWM would not have the monogram. DWM was already using the well-known monogram in 1909, i.e. right from the start of P08 mass-production.
(Source: Joachim Görtz, "Die Pistole 08", 2nd Edition 1988, P.99)
The expert books on Lugers are those by Jan C. Still. These seem to command solid 3-figure prices, and I am reluctant to spend as much on a couple of books as my LP08 cost. I have to make do with Görtz, who has an interesting discussion starting on P.131 about the problem of estimating how many P08s (and LP08s) were actually produced up to 1918.
The vital point has already been made - all quoted number ranges are observed ranges, not factory records.
It seems (Görtz, P.136) - from recorded serial numbers - that DWM manufactured about 130,000 P08s in 1915 alone. Now the standard Germanmilitary numbering system at that time was 4-figures from 1 to 9999. Then 1-9999 with an "a" (lower case) suffix, then "b" etc round the alphabet (but not, I think, using all letters). The observed range previously quoted - from 1398 to 3850d would thus only cover some 44,000 pistols and is totally inadequate to cover 130,000 units.
If the factory serial numbers also included LP08 and P04 (marine) Lugers, then the ---- d number could be from the 2nd time round the alphabet! As could, of course, your 11xx number.
In short, the numbering system became ambiguous under wartime mass-production! That is the second reason to be unimpressed by the claims of that "collector".
But these are just the comments of a shooter, not a "collector". Others who are better informed (Still?) can surely add more. I suggest that you search in Jan Still's Luger forum
Jan C. Still Lugerforums
for the "state of the art" in this matter.