You may want to contemplate doing the Italy leg on a different weekend. You'll probably need to pay the stopover charge but it makes life easier. You also won't have to drag checked baggage to Italy, assuming you're taking a case to Japan with you. (If you are taking a suitcase, then you need a LOT more flexibility in your schedule since you need to collect it, go landside and drop your bag off again.)

Isn't it Linate that tends to have serious fog issues in Winter? Others can confirm. If so, it again makes a quick turn difficult.

Last time I did this, in May, I stayed at the Hilton at Rome Airport overnight - its connected to the terminals. However, I used points for this - its not a bargain otherwise. I then flew to the UK the next morning and got a 3pm flight onwards.

First time I did an ex-Italy, we did a weekend in Milan about 6 weeks before the long-haul and paid the stopover fee. I've got the Missoni scarf I bought on that trip with me today, actually!

To be honest, getting to Italy and getting back in time for a 14:35 flight to Tokyo is going to be tricky without an overnight stay. And, if you're paying for the hotel, you might as well NOT pay for the hotel by making Italy a day trip and then paying the BA stopover fee instead.

If you do decide to do Italy on a separate journey, this obviously opens up Venice, Bologna, Naples etc as well as possible starting points. If you've got some hotel points to burn, you may want to look for somewhere you could burn those.

For what its worth, when I went to Japan I did it on an ex-Vienna ticket and did an overnight in VIE before flying back and heading straight down to NRT (handbaggage only). Its quite easy to do in VIE as the airport train drops you in the main hotel district with the Hilton opposite and the IC just a short walk across the park.