There are major differences between a Model 2 and a Model 53. The Model 2 is essentially their mass produced and very popular "good quality" sidelock gun, the Model 53 is also a sidelock gun, but a "Top Of The Line" one at that. To someone that knows the differences, the distinctions are immense. The Model 2 has been an extremely popular "mass market priced" gun, better than some of their lower grades, and a good field gun, but the Model 53 is in a different league. It is essentially a scaled down "field" version of their Model 56 competition gun. If you didn't see gold plating (washing) on the lock parts you removed, there's no point in taking off the other one, it's not a Model 53.
Can you post photos for a positive identification?