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Hit the Credit Pulls Database and see what scores were denied for the card you're interested in. If you see a handful of scores denied that are at or above yours, it's probably not wise to apply. If you see lots of people approved with scores at or lower than yours, it would make sense to give it a shot. This is honestly the best way to access real data points above and beyond just what forum members here "feel" may be the way to go.
I think you could pull the trigger now. If the baddie is almost 7 years old, it has absolutely no effect on your score, especially with other CO accounts still on your report. The only way it would make a significant difference is when the last one falls off and you are rebucketed, then, in my case, i had seen almost 50 points jump on my TU score overnight. Besides that, you will not see any difference in your score because the CO is very old. If you do Delta, you will probably get approved for $1000. Then use it for 4 to 6 months, and generate seom internal score with Amex, then apply for BCE. You will get it in a heart beat. You can go for the Delta and Green on the same day, back to back.