Thanks guys.
I decided to go to Birmingham because it was on a Friday and I could take a long weekend and see some people I know in Birmingham as well.
It took nearly 3 hours in total. After looking at the documents, phoning around, checking past records and taking the payment they told me it would take from one to one and a half hour because there were 3 passports. It took about 2 hours after that, but never mind. The important thing is that ILR was granted in the end. The people were very polite and friendly throughout, including the security guards. I think a smaller PEO does help in that way.
The lady who checked my documents was a bit light on knowledge of exact requirements though
She asked me to show a recent letter from my employer, although I applied in HSMP category. She said that the offer letter for my current job was not good enough as it was nearly 3 years old. I told her such a letter was only a requirement for applicants in WP category. She said she needed a proof that I was still employed. I pointed towards my payslips and bank statements but she said "your ex-employer could owe you money from the past and you may not be working there anymore". A far-fetched but (sort of) believable idea. I told her that I had resigned from that company and was doing my notice period for a few more days only. Soon after which I was starting a new job for which I showed her my employment letter and contract. She said the next job was not significant and because I was still employed by my current employer, she needed a recent letter from them. Anyway there was no point in arguing, I had a bag full of documents and I dug out a letter regarding my share options in my current (soon to be ex-) company. Completely irrelevant I know, but she was happy. Even if I had asked, my employer could not have given me a letter saying "he is still employed by us and we still need him" because I was leaving soon.
I have read a similar story from another HSMP->ILR applicant on this board so I would advise people to get a letter from the employer anyway. Not because it is a legal requirement but because you might need to satisfy someone who doesn't know his/her stuff properly.
All in all, a good and recommendable experience that saved me from weeks of anxious waiting.
Good luck to everyone!