I think you first instinct to get close to a potential attacker is not too clever.By getting close to a person this allows the would be assailant an opportunity to attack you.What would you do if a knife was involved?Judo is good , however the combative distance is too near.The minute you get near [within arms length] you immediately become vulnerable to kick/punches/knee in the groin and the Glasgow Kiss[head butt].
My own personal strategy on being faced by an angry chap is to be all sweetness and light and at the same time check out if there happens to be a 4 by 2 available if charm does not pacify the opponents raging spirit.
And the minute I get "without" arms length they have the range to pull their gun and shoot me. I live in Indianapolis, not the UK. I've never seen someone with a knife here, but I've seen plenty of guns.
In regards to cross-training. I recently tried Kendo for the first time and it made me realize how bad my Iaido is...