If you've booked separate tickets for the two legs of your journey from Tashkent to Tokyo then the airlines won't automatically transfer your baggage from one flight to the next. You'll need to reclaim your bags and check them in for the next flight. This will require you to pass through immigration*.
As Uzbeks you will need a visa at Incheon airport to enter Korea.
You asked if booking the tour will allow you to get to your bags. If the tour was 'airside only' then it wouldn't. However, the tour does allow you access to the places, restaurants and shops, but to do this you have to enter Korea by passing through immigration and that requires you to have a visa. The tour won't help you.
You could ask Uzbekistan Airlines if there's some way that they can transfer your bags for you. If there is, they may charge you for the service.
Otherwise, you'll need a visa.
* I found one post on TripAdvisor that suggested you can claim and re-check your bags in the transit area, but I haven't been able to corroborate it.