I would look at manually importing them. Write your own script, there is an example in the readme something like
User.order('created_at DESC').find_in_batches do |batch|
Tire.index("users").import batch
end
Or use their import tool:
User.index.import User.order('created_at DESC')
If your site is widely used I would would be tempted to spin up a different core or instance of solr, import everything and then switch your app to use the new one.
Hope that helps.
Edit:
If you are using rails, then make sure you include your rails environment in the script (config/environment). If it is going to take a long time to import then you might want to run the script with 'nohup ruby my_script.rb > script_out.log 2>&1 &' so it isn't bound to your ssh session.