Welcoming is more than a one man job. The whole eldership should be on the lookout for the new, the returning and the occasionals. And then, one of the main purposes of the weekly(?) elder's meeting is to to review the new, returning and occasional folks from 'last Sunday'. Many eyes see more than one or two pairs. In a larger fellowship (and 1000 counts as large), one elder will see or hear, or 'read' a visitor different from another. You get the 'Chuck seemed down. Oh? he seemed quite bright to me...' sorts of conversations.

But its good to encourage the entire body to welcoming (of course!).... So that's the official welcomers, and stewards, but also the person in the pew(chair). Occasionally its good (and amusing) to say from the front, 'If the person next to you hasn't said 'hello' ... Maybe they're a visitor as well?' ... It breaks the ice and eases people in to conversation.

Another trick to creating a welcoming tone and style is introductions. If you can get out of a visitor a titbit of information, origin, work, something, you can often then introduce them to someone else in the body who overlaps their world. 'Here's Mike, he's from Wisconsin too' ... But introductions also mean instant connection in the place, and next week, they'll not see some welcomers and 990 strangers, they'll see a dozen new friends.
The plural of anecdote is not evidence.