I played with my 5y old daughter using the Ticket to Ride: Europe base game and the following house rules. (We played twice; each game taking 20-30min.)
The first player to complete 4 tickets wins!
(We don't use the score track)
Deal four train cards to each player
Everybody play cards face up
Remove all destination cards higher than 8 points ...
You cannot trade destination cards at all: neither the ones you receive at the start nor any you receive later.
You get three at the start and can choose to keep all three or just two (discarding the other one). Rulebook:
Shuffle the Destination Ticket cards and deal 3 cards to each player. Each player
looks at their Destination Tickets and decides ...
With six players the map might become a little too cluttered quickly: rather than adding new rules that make the game fiddlier, I would rather reduce the number of coaches, probably between 35 and 40. Hence players would focus on completing fewer tickets too: consider scrapping the longest tickets, which could become difficult to complete.
On a side note, ...
With 6 or more I would split into 2 games of ticket to ride since with 5 players the down time is already pretty high to keep player interested in my opinion. I do think it is possibly to balance the mechanics of the game but the down time between plays would make it a very slow game and not the best for that size of group. Part of what makes a game ...