Having ties in Ontario is not a mandatory requirement under OOPNP to obtain a PT. They haven't clarified on the parameters for converting a PT to PN but it appears to be a FCFS system so getting your application in asap should be the highest priority.
About ties to Ontario, this is what they ask for...
http://www.ontarioimmigration.ca/en/pnp/OI_PNP_EE_CAPITAL_APPLY.html#display
Job offers or jobs applied/interviewed for in Ontario
Volunteer work in Ontario
Lease agreements for a residence in Ontario
Professional networks
Family ties
Personal relationships
Try to apply using online job boards to secure interview call(s), trawl through your LinkedIn network to see which friend-of-friend can be added at short notice and spend time on your social media networks to identify the slightest Canadian link and expand on that.
However, none of these are really foolproof ideas at such short notice. The next best alternative is to write a nicely worded letter of explanation acknowledging upfront about the limited nature of your ties to Ontario and trying to convince them about your intent to contribute to the province as a Permanent Resident.
All the best!