Definitely reapply. I work public sector and have shortlisted and interviewed plenty of times. We would not know if someone had reapplied as all applications are anonymised and no personal information is included.
Definitely write a supporting paragraph or two under each essential criteria. The way shortlist is, each criteria has a score of 0, 1, or 2. 0 if you don't meet it at all. 1 if you can show examples of meeting the criteria. 2 if you excel at showing how you meet it, with multiple examples. For example, in almost all of our roles, we have a criterion about being competent in the use of Microsoft packages and other software systems.
A response with a score of 1 would be something like, I am proficient in the use of Microsoft packages. I have experience of using Outlook for email and calendar management, Word for word processing, such as reports or letters, Excel for databases, and PowerPoint for presentations. I also have experience of other software packages such as X and X.
This kind of response would show that the candidate knows what the packages are and what they're used for.
A response that would get a 2 would be something like, I am proficient in the use of Microsoft packages. I have extensive experience of using Outlook for email and calendar management. I am familiar with the additional features in Outlook, such as programming emails to send at a certain date/time, creating email templates for repeated emails I send on a regular basis, creating distribution lists and colour-coding the calendar for easy identification of meetings.
I use Word regularly for processing letters and reports. I am knowledgeable on using the enhanced features Word has to offer, such as tracked changes, mail merge, password protecting documents (etc. etc. etc.)
Obviously this is all repeated for each package you're familiar with. There's a fine balance between writing too much and them getting bored, and not writing enough so that somebody else pips you to the post and gets that extra point which secures an interview. Sometimes, we can get a lot of applications for a role so we'll only take forward people who score a mark of 2 on every criteria. So write down as much as you can for each one.
Good luck xx