This is a 'Foote Model 35' gearbox, and the issue with old grease has been documented - here's a good rundown;
https://www.gilsonsnowblowers.com/snowbulletins/gsbs_01.pdfIt's not that the original grease used was 'overkill'; it was Shell Darina '0', a bentonite clay thickened, NLGI #0 grade, Extreme Pressure semi-fluid grease, as per the chart below. It has just 'gone off' over time, and lost its flow properties.
I would tend to follow NormK's advice, and use an 'NLGI 00' grade grease, which is a bit more 'runny'.
For example, Penrite 'semi-fluid grease' is an NLGI 00 grade EP grease, which is available in 450g cartridges. Most of the other manufacturers' 0 and 00 grade greases are only available in 2.5kg and up pack sizes.
Good rework of those gears, BTW. They have been unavailable new for a few years now.