I can confirm that I got into top programmes without any publications, but very solid rec letters (and generally stats similar to yours). In my experience, if the professors know and respect your rec letter writers, they care about that a lot more than publications, because they understand that it's hard for undergrads to have publications (especially in 10 weeks, and by your senior fall). In fact, they take into consideration if you took time off and hold you to a higher standard. In terms of which programs to apply to, I'd recommend applying to a mix of quantitative programs and umbrella programs (e.g. Harvard's BBS program). These programs give you the same opportunities to take computational classes/ do computational work, but may be easier for you to get into.