RiceCrispieTreats, I've actually just had a reeeaaallly long phone call with my best friend of over 20 yrs who lives at the opposite end of the country to me - she voted Remain, I voted Leave.
I spoke to her at length on Friday too after the result came out and she was very upset, whilst I was over the moon.
Speaking to her on Friday really helped me to 'get' her side of it & emotional reaction as a remainer which was great for me to keep perspective and to understand more; she told me today that she had felt the same after talking to me too.
Anyhoo, today we had a long chat about it all and she said pretty much what you have - for her the EU was keeping our awful politicians in check and forcing them to do the right thing (working time directives / gay people in the military etc).
For me, the EU was a parent that I didn't want, treating the UK like child that needs to be kept in check - what I wanted was for our country to govern itself properly with no interference.
Our ultimate goal was the same though - like you, we both want to work & collaborate with Europe & the world, we both want refugees to be welcomed, helped & homed, we both want free movement of workers, we both want redistribution of power & economic wealth across Britain, we both want social justice, we both want our politicians to be honest & to represent the whole of their electorate the very best they can.
What divides us, however, is what we believe to be the best way to achieve this.
She thinks that to remain within the EU.
I do not.
I see the referendum as the first part of the battle; the people spoke and made their voice heard.
Now the political elite who thought themselves untouchable are in turmoil and are imploding spectacularly.
There are a whole raft of amazing up & coming MPs from the 2010 intake who have more than hit the ground running in both main parties, and they are the ones who can bring about the long overdue change to our politics.
This is the second part of the battle in my mind.
Get these people in the cabinet & shadow cabinet & elect 2 strong, principled leaders - not from 'the old guard'.
I truly believe it can be an amazing outcome, but unfortunately the downside is the economical side of things.
I know there will be pain short to medium term, but I truly believe that long term we will be significantly better off.
Hope that makes sense?! 