4000 fps I haven't attained yet, nor had a rifle capable of trying to do it, but I have gone to 3500 fps with very safe loads using a 170 gr bullet in 30-06. This with my glue on patch bullets.
Based on this performance and customer feedback, I believe your goal is attainable, or close to it, and cost per bullet is near nothing. However, one has to have patience to handle such tiny bullets as 22 and smaller with paper patching. You can read more about my GOP bullets in quite a few posts on this forum, most and perhaps all of which will be questions about paper patching, because I always mention GOP in any such questions. Also on my website, LBTMoulds.com