From my own experience of motorcycling in Africa, although not specifically Uganda the only paperwork customs are interested in is the carnet and I advise speaking to the most senior Uganada customs officer you can find at the border and explain why the bike was left there and try to get them to stamp your current but expired carnet out of the country and take the bike to another who will let you enter on a temporary importation permit, I believe Kenya might do this.

I realise that in theory a vehicle should be legal in country of origin with a current registration/road tax, safety/MOT test but it is not always possible to keep this up on the road and people continue their trips with them expired, it is between you and your conscience as to whether you do this, it obviously could also cause problems if you have an accident but with many border crossings all over the world I have never had this checked, except entering Australia.

As long as you have a registration document/title with the bike's details and a matching number plate on the bike you should be able to continue either to a port to ship the bike home or onward through other east and southern African countries if you want, if you are not comfortable riding it with expired registration you could have it and yourself transported to a port to get it removed.

I expect you will have to bring the bike back into Australia to get your carnet deposit back and to ensure no claim is made against it which could cost you a lot.