[CMOTD]

how would one install a solid front axle ?

With some difficulty! It really needs a revised front end as can be seen from post #48 HERE on SFI from Graham.

I suppose the question is whether you want to turn it into a proper racer or are happy to run it as is with all its faults and charms. If the former then you might as well throw everything away apart from the body and start from scratch. If the latter then the wobbly front wheels won't make a lot of difference to the overall performance as the rest of it is so poor. The motor is terrible and the carbon brushes are unique and unobtainable as spares.