5 mm is a good size. Smaller nozzles create a problem for the pumps in such cheap hot air stations. The small nozzle means pressure is building up in the system (as evident by your observation that you have some 'blow out'), and the cheap pumps can't work well against that pressure - reducing the maximum airflow you can get out.
Fixing your 'blow out' should increase the airflow a little bit, but won't make a huge difference. These nozzles are typically of rather soft material, so you should be able to bend the 2.4 mm nozzle into some better shape to sit a little bit tighter. Also check if you have other leakages in the air system. But see above.
350 °C is also a little bit low. On a professional, well regulated station one would typically start with 400 °C, and 20 l/minute air flow. But scales, displays and regulations on these cheap hot air stations are such that what is shown on the displays or scales is not what is going on. Especially the airflow is not regulated.