We run into the same issues; generally playing with 7-8 people.
There are a few techniques we use to help: Players don't keep their own cards immediately in front of them; they keep somewhere in between their own seat and the center of the table.
Close enough that it's clear whose is whose.
I try to start the night phase already leaning forward, so that if I don't make noise leaning forward if I need to later.
Even with doing these things, taking actions that involve other players' cards such as seer, troublemaker, or robber, are generally just restricted to choosing a player that is seated close to you.
As a seer, I would never attempt to look at the card of a player sitting across the table from me.
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There are two ways I can see going about this.
Change the order players go in to be based on seating order
(this is how one night resistance works) so that everyone goes in a set order.
Also as part of this have everyone get up and walk around the table that way you can't tell what someone does based on getting up or not.
When doing the night phase have everyone stand up and move away from the table this way when people are called to do their step they can move to the table and do their action in a less delectable manner.
Note #1 will mess with balance at times do it the order of actions changing based on how the deal lands but as long as everyone plays the roles of how they where at the start of the night it is possible it won't mess with balance to much.
This is how One Night Resistance handle roles and they have similar actions to the ones in this game.
boardgames.stackexchange.com/users/5001/Joe W
Note that one does not need to use a ten-seater table to play ONUW with ten people.
There is only need for enough space to fit the centre board plus the cards of each player in a ring.
A table or desk with dimensions of a metre each way is more than sufficient.
The players' seats are pushed out away from the table when conducting the night phase.
Each player then has space to move forward, perform their actions, and lean back again.
It can be more helpful to stand during the night phase if capable; the table can be put closer to those that require seating throughout.
If you so wish, and are resourced enough, markers can be taped or stuck to the table to indicate which card belongs to which seat, to avoid unnecessary confusion over what is moved where or who may look at which cards.
This has served for groups up to twelve, including relative newcomers and casual players, and could reasonably extend to groups of 15-16 without much more difficulty.
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I have played one night werewolf with 10 people on many occasions.
Here the three things we have done that made it work well.
Note that tips 1 and 2 are useful even at lower player numbers.
Have everyone stand before the night phase.
If you are playing on the floor, have everyone get up on their knees.
This way, players can reach all of the cards without moving substantially and/or making noise with their chair.
Move all the cards towards the middle before the night phase.
The cards should be in a fairly tight ring around the middle three cards (though not so tight that you can't tell whose card is whose).
If you don't do this, players usually can't reach the cards of players across from them, and so will only look at or manipulate cards of people near them.
Don't use a table that seats 10.
If you're using a table that can comfortably fit 10 chairs, your table is too big.
Your ideal table is one that comfortably fits six.
If you have an adjustable table, take a leaf out of the table or fold in the wings to make it smaller.
The key here is that you don't actually need all that much play space, and players don't interact with the pieces during the day, so can have their chairs a bit back from the table to fit (since they are standing during the night phase).
The other option is to play on the floor if you have a large carpeted area.
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Use a referee for large games.
Then you can just point at the cards and the referee (standing) can move around the room a lot and reach in to the table without actually showing anything during the phases so that people don't know which cards were shown or to whom.
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We were playing with only 6, and we found it is virtually impossible to reach for cards across the table without making a lot of telltale noise. I opted for crowding in and keeping my arm raised on my elbow so that I could reach any card just by lowering it.  How can 10 people gather around the cards and take their actions without most of the table knowing?  What do  you  do?
How it is physically possible to play ONUW with 10 players?
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<one-night-werewolf>
boardgames.stackexchange.com/questions/44235
boardgames.stackexchange.com/users/25651/DaveC426913
Players don't keep their own cards immediately in front of them. You can also stand during the night phase. Stick markers to the table to show the cards that go with each seat. You do not need to use a ten-seater table to play ONUW with ten people, an ideal table is one that comfortably fits six. Markers can be taped or stuck to the table to indicate which card belongs to which seat. Players shouldn't keep their own cards immediately in front of them, but keep somewhere in between their own seat and the center of the table. Everyone should get up and walk around the table so you can't tell what someone does based on getting up or not.  It can be more helpful to stand during the night phase. S4: If you are playing on the floor, have everyone get up on their knees.  
Players shouldn't keep their own cards immediately in front of them, but keep somewhere in between their own seat and the center of the table. Everyone should get up and walk around the table so you can't tell what someone does based on getting up or not.  It can be more helpful to stand during the night phase. S4: If you are playing on the floor, have everyone get up on their knees.   You do not need to use a ten-seater table to play ONUW with ten people, an ideal table is one that comfortably fits six.  . Markers can be taped or stuck to the table to indicate which card belongs to which seat. The cards should be in a fairly tight ring around the middle three cards . Use a referee for large games.