Defaulting on all Euro debts, exiting Europe, bankrupting the banks, issuing a new currency is a viable solution. Yes it's a horrible hang over to live through but it means removing the horrendous debt burden for the next 50 years. See how Greece is having trouble with every IMF payment in the past few months? If the EU has its way Greece will continue paying chunks of cash like those for decades to come. Better to burn everything down and start over. They might even pick up some Russian and Chinese financial support along the way.
"floating to", "floating with", "floating against" is a minefield.
There is always the danger that Greece will say "to Hell with it," print money to fund their expenditures, and get hyperinflation. But that's a level of mismanagement even worse than Greece has shown in the past.
If they do not tend the root of the problems, they might as well do this every 50 years. Things like 14th month payments (while it was a thing) or tax evasions that could reach industrial levels on their own will make things hard, even without the IMF or EU interfering.
Germans have to work to 69 now and get less than the average Greek retiree.