Using User Stream to get older tweets

I am programming an application which collects special tweets containing a special keyword using Streaming API (Firehose).
My application is divided into three steps:

1) Get all Tweets using a special keyword using Streaming API (Firehose)
2) Get all Users which are contained in the collected tweets
3) Get all other tweets of the User (tweets of the last days + the future tweets which the user will tweet)

HOW IT WORKS:
1) This works pretty well.
2) This works also well.
3) There I have a real problem.
In my database I have all the appropriate users and with a loop I check in a background process if the past tweets (max 3200 tweets) has been collected.

If the past tweets have not been collected yet I do this with the api.twitter using the user_id
(https://api.twitter.com/1/statuses/user_timeline.json?include_entities=true&include_rts=true&user_id="XYZ"&count=3200")

If the past tweets have already been collected I use the api.twitter using the since_id argument to get the tweets since the "since_id"
(https://api.twitter.com/1/statuses/user_timeline.json?include_entities=true&include_rts=true&user_id="XYZ"&since_id="XYZ")

PROBLEM:
Step three is implemented with a background process which collect all tweets (the last 3200 + the current and real-time tweets) from each user which is stored in the database. The problem I have is that I am using the api.twitter to get the tweets for a user. So if I would have thousands of users I would have thousands if requests using api.twitter, but there is a limit of 150 request per hour. This is the problem I have.

QUESTION:
Is there a way to use the User Stream to get user's old tweets from a time frame using since_id?

Thanks!