You can do this without hitting limits for a single account.
A timeline only has 200 tweets in a single call, statuses/lookup.json allows you to manually lookup 100 statuses at a time.
It’s unlikely all 200 tweets in a single request will all have quoted tweets in them. It’s a good stop gap until quoted_status is added to the API directly.
I’ve been using this method for weeks with no rate limit issues.