First off, the fuselage of this model is way too short for the type of modification Boeing made to the wings, to be able to fit a bigger engine.

The 737 was designed as a replacement for the Boeing 727. It entered service in 1967 as the 737-100.

Over the years, it has gone through several generations and variants, each improving and updating its features to meet airline requirements without tampering with its center of gravity.

In 2001, larger engines were introduced on 737 models and this brought huge problems and implications that caused instability during climbing specially.

Boeing, instead of addressing the root of this problem, they implemented a new software causing the elevators to activate to fix the high rotation issue without sounding any caution alarms in the cockpit to let the pilots know this was actually happening.

To fix this problem, Boeing need to redesign an engine specifically for this model and sacrifice profit that other larger engines could offer or;

Instead of placing the larger engine higher and forward, the problem could be solved by adding 757 landing gear to make the fuselage higher off the ground.  This will allow the larger engine to be in the same place and avoid center of gravity issues.

This will eventually avoid the need for further pilot training and aircraft certifications.