Yes, for some reason (post count too low?) I can neither insert a link nor paste the address in, but the IRS has a page for "New Methods for Correcting Elective Deferral Errors". It includes a link to Rev Proc 2015-28 with the details. If you fall under the "early correction" criteria the correction would be a QNEC for 25% of the missed amount -- which, as you said, is easy to determine. Matching contributions with lost earnings are also due, and an end-of-year discretionary matching contribution, if any, would be calculated based on the deferrals they would have made had their election been followed correctly.
Participant notice is also required, and the rev proc specifically addresses your question about participants having the option to increase deferrals; specifically, the notice must include language saying exactly that.
[Edited: Sorry, for some reason I thought there was a model notice available as well. I must have imagined it. That's why I try not to rely on my memory!]