The advantage of euro currency is the 500 bill!
A lot of money in 500 bill take up little space compared to the same amount in 100 $ bills! 
I never had any problems traveling between different countries.
Once I passed the border between Croatia (NON EU) and Slovenia (EU) with over 100k in my bag.
I was lucky to not have been discovered.
And then entered in Italy, between Slovenia and Italy the border no longer exists.
If you do not want to risk you can buy jewelry or declare the winning tu customs (and pay taxes).
If money comes from the casino is “clean”. So why be afraid?
Casino also may issue a winning receipt, if the player asks it.
Bump
When i was playing poker full time i used to come across this issue, having to travel with large portions of your bankroll in cash for higher nl games and a 10k au customs limit is a pain in ass.
Westernunion bank deposits are an option, 2-3 days to process max and your winnings are avaliable for future withdrawls if need be, just make sure to keep all your casino recipts as cash transactions over $10,000 are flagged and may requiring explination come tax time. If you want to avoid banks i believe you can setup a western union account also like a pseudo bank account for border crossings or worse to worse if you know your destination can send the amount to yourself at your future destination.
Anoymous prepaid visa only come in $100 limits which is more suspcious than cash lol. With a company account i belive you can load up too $50k.
Cheques for amounts over your allowed br is best option just have to be careful not to tie up too much cash encase you run bad and don’t have the option of cashing the chqs.