If you did not apply through Arsenal America it may be too late. Since you all ready have red memberships make sure all your accounts are linked so one person can purchase all four tickets. You will not be able to purchase tickets until 30 days before your match. Tickets go on sale from Arsenal at 10AM GMT so figure that time difference for you get up early and hope you can be in that first 3,500 (RED level tickets made available for each home match). I was able to get tickets this way for the CL match on 10.19.16.
A more expensive approach but guaranteed is to use an official Arsenal Ticket Club Level reseller. http://www.arsenal.com/fanzone/official-overseas-club-level-agents-2013/14
I have used http://www.ticket2football.com and they are great. The tickets cost a lot more but you can buy them as early as you want. You also get some perks like a Stadium tour and a program and free halftime drinks. (Club Level package incl. Business seats at Club Level, access to Club Level bars and restaurants, halftime drinks, match program, voucher for Stadium Tour & Arsenal Museu, 5 GBP gift voucher for Arsenal Shop – Seating together.)
There is also the Arsenal ticket exchange where season ticket holders can put up their tickets for sale. Never tried this but I imagine it might be hard to get four seats together.
You may have figured this all out all ready, but maybe this will help anyone in the future.