It is easy to model tiger 131. It was captured in April 1943 and has a camo pattern with RAL7008 and 8000 both chipset acurate paints can be found in Vallejo Model Air range and are accurate for Afrika Korps Armour for 1943.
the decals in the Tamiya kit are wrong, but research shows what the real 131 numbers look like and these can be got as AM decals and I do believe that AFT should provide the correct numbers availabe in their dry rub on set (they look like painted on numbers when applied) in this set:
http://www.archertransfers.com/AR35042R.html
You may be able to modify the Tamiya kit to represent Tiger 131, but I think that maybe you should look at RFM's kit RM-5025 with Friul tracks
http://www.friulmodel.hu/en/atl-25-tiger-i-early-i29/
Aber's metal barrel to replace the kit one should be fine.
http://www.aber.net.pl/detal,1475.html
You can alter parts to fit walkrounds of Tiger 131 and photos of it after capture. Tamiya Tigers are not really accurate but with time and alterations a reasonable job can be done!
Of course, making a model of what is one of the most famous Tiger I's needs a personal visit to appreciate the size of the thing and a good close up inspection of this beast because people who view your build when finished automatically become a "Tiger Expert" and will start picking holes.
Somewhere, maybe in German archives or out there on the net will be photos of when this vehicle had just arrived in the desert with a brand new paint job etc. Germans were really good at propoganda.
Good luck with the build