Based on your timeline, the first refusal that's a lot common (R.10 Check) would have had happened by now if the completness check officer wouldn't have accepted your PCC for the time being. However, now it all depends upon the final reviewing officer to accept, refuse or ask for a new PCC. With the limited operating capacity of PSK's in Punjab, it might take a long time (30-60 days) for you to get the PCC. You can even get it early provided you follow up with them closely and request them to expidite the process. Beleive me, I have seen the whole process being completed in a day after the PSK intimation to the local Police Station.
If at all, you decide to go through this route, there are only 3 PSK's operating at the moment and you might want to check if they accept applications for other districts.
Without wasting any further time, call up IRCC and ask for the status of your application and ask them specifically about Eligibility, Security, Background checks. Based on the conversation, you can jump start. Never the less, try to get a PCC from PSK. You never know when that might come in need. Also, if you see that Security and Eligibility hasn't been passed till now, send a LOE to the Officer letting him know that you're in the process of procuring the PCC so that they delay your application rather than refusing it. Good Luck.