They are apparently 10 months old, so I'm not sure if they can be processed now if we decided to, or if they need to be older
You can slaughter and eat a bird at any age.
Don't think sexlinks will ever have much meat on them.
I slaughter my cockerels at about 14 weeks.
I agree that your coop is small for 15 birds...especially when integrating birds that had not lived together previously.
Here's great article on......
http://www.backyardchickens.com/a/how-much-room-do-chickens-need
Here's some tips on....
Integration Basics:
It's all about territory and resources(space/food/water).
Existing birds will almost always attack new ones to defend their resources.
Understanding chicken behaviors is essential to integrating new birds into your flock.
Confine new birds within sight but physically segregated from older/existing birds for several weeks, so they can see and get used to each other but not physically interact.
In adjacent runs, spread scratch grains along the dividing mesh, best if mesh is just big enough for birds to stick their head thru, so they get used to eating together.
The more space, the better. Birds will peck to establish dominance, the pecked bird needs space to get away. As long as there's no copious blood drawn and/or new bird is not trapped/pinned down and beaten unmercilessly, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.
Multiple feed/water stations. Dominance issues are most often carried out over sustenance, more stations lessens the frequency of that issue.
Places for the new birds to hide 'out of line of sight'(but not a dead end trap) and/or up and away from any bully birds. Roosts, pallets or boards leaned up against walls or up on concrete blocks, old chairs tables, branches, logs, stumps out in the run can
really help. Lots of diversion and places to 'hide' instead of bare wide open run.
This used to be a better search, new format has reduced it's efficacy, but still:
Read up on integration..... BYC advanced search>titles only>
integration
This is good place to start reading, BUT some info is outdated IMO:
http://www.backyardchickens.com/a/adding-to-your-flock