Using nailpoints =ListtOfNailPointsTotal one can use the following to create a framework to actual create the string image using the nails numbering as seen this file image....

umberofNailsUsed = Dimensions[NailPoints][[1]] (* 979 *);
xvalues = Table[i, {i, -170, 170, 4}]  (* 86 *); 
yvalues = Table[i, {i, -220, 220, 4}]   (* 111 *); 
PointsaroundFrameBottom = 
  Table[{xvalues[[i]], yvalues[[1]]}, {i, 1, xno}];
PointsaroundFrameRight = 
  Table[{xvalues[[xno]], yvalues[[ j]]}, {j, 2, yno}];
PointsaroundFrameTop = 
  Table[{xvalues[[xno - i]], yvalues[[yno]]}, {i, 1, xno - 1}];
PointsaroundFrameLeft = 
  Table[{xvalues[[1]], yvalues[[yno - j]]}, {j, 1, yno - 1}];
ptsaround = 
  Flatten[{{PointsaroundFrameBottom , PointsaroundFrameRight , 
     PointsaroundFrameTop , PointsaroundFrameLeft}}, 2];
nopts = Dimensions[ptsaround][[1]] ;
pointswindex = Table[{i, ptsaround[[i]]}, {i, 1, nopts}];
ppdts[i_] := pointswindex[[i]][[2]]  (* points around the frame !! *)
               framepoints = Table[ppdts[i], {i, 1, nopts}];
pt = {102, -220}; ptext = 4;
(*ListPlot[   framepoints,AspectRatio\[Rule]220./170. ,Epilog->{  \
Black,PointSize[Large], Text[ptext,Offset[{0,-5},pt]]} ]*)
alignn1 = Table[{-170 + (i - 1)*4, -220}, {i, 1, 86}];
 textn = Table[Style[Text[ i, alignn1[[i]] , {0, 3}], 4], {i, 1, 86}];
alignn2 = Table[{170, -220 + (i - 1)*4 }, {i, 1, 111}];  
 textn2 = 
  Table[Style[Text[ i + 86 - 1, alignn2[[i]] , {-3, 0}], 4], {i, 2, 
    111}];
alignn3 = Table[{170 - (i)*4, 220}, {i, 1, 86}];
 textn3 = 
  Table[Style[Text[ i + 86 + 111 - 1, alignn3[[i]] , {0, -3}], 4], {i,
     1, 85}];
alignn4 = Table[{-170, 220 - (i - 1)*4 }, {i, 1, 111}];  
 textn4 = 
  Table[Style[Text[ i + 86 + 111 + 86 - 3, alignn4[[i]] , {3, 0}], 
    4], {i, 2, 110}];
framenumbers = 
  ListPlot[   framepoints, AspectRatio -> 220./170. , 
   Epilog -> {  Black, textn, textn2, textn3, textn4} ] ;
alignn1;
alignn2[[2 ;; 111]];
alignn3[[1 ;; 85]];
alignn4[[2 ;; 110]];
Dimensions[NailCoordinates];
  NailCoordinates = 
  Join[alignn, alignn2[[2 ;; 111]], alignn3[[1 ;; 85]], 
   alignn4[[2 ;; 110]]] (* 394 *) ;
Dimensions[
  NailCoordinates](* \
NailCoordinates=Join[alignn,alignn2,alignn3,alignn4] (* 394 *);*);
Dimensions[NailCoordinates];
image1 = 
  ListLinePlot[
   Table[NailCoordinates[[NailPoints[[k]]]], {k, NumberofNailsUsed}], 
   Frame -> True, ImageSize -> 500, 
   PlotRange -> {{-170, 170}, {-220, 220}}, AspectRatio -> 220./170. ,
    PlotStyle -> {Thickness[0.001]}  ];

 Show[framenumbers, image1] 
---------------------------

Nicely done and very interesting, thanks for sharing! It is somewhat related to an old post of mine:

Knitting images: using Radon transform and its inverse for creative arts

but I disregarded fixed nail points.

Note. At the end of the program, you can Manipulation such that it allows one to see the treading of the image. Open up the control by clicking on + and the click on the + under the k line to step slowly through the beginning to see the connections. This will show the step-by-step stringing process.