To stop people from parking on the square, they could allow some of the restaurants to set up satellite patios in the warmer months, like they do in Europe, then you know for sure that cars will never park there. But for this to work, you need to have lots of clientele to fill up the existing patios first.
Here is a nice example from Warsaw, notice how there are streets between the patios and the restaurants, which the servers have to cross, which only have local traffic on them.
https://stowaweigh.files.wordpress.com/2011/06/img_1035-1024x375.jpg
http://www.masterfile.com/stock-photogra...Town-Market-Place-Old-Town-Warsaw-Poland
Another idea is to build a funky fountain in the middle of the square, lit up in the evenings. That could also stop cars from parking there.
This is just the tip of the iceberg, there are loads of ideas, the people working for city of Ottawa and OSEG simply need to tap into their imaginations.