You don't need proof of address, you only need to prove your residence.
You don't need to send the bank statements if you are sending P60, that's just increasing the amount of paperwork.
I used HSBC bank statements (duplicates that I also got from them for £10), no problem there. I got them in the post and they said 'duplicate statement'. A duplicate is not a photocopy (they do look like originals as well) so it's all good with HO.
Best to keep your application light (but of course still send unimpeachable evidence). I for example sent:
Year 1-3 (Worker): 3xP60 and 1 employer letter (proves treaty rights and residence)
Year 4-5 (self-sufficient and later worker): 3x bank statements (HSBC as above) and 1x utility bill and CSI proof (self-sufficient) ad then 2xP60 and employer letter when I was a worker again. All in all about 10 pages. Don't stress too much, your evidence sounds good
All information given is just my opinion as a member of this forum and does not constitute immigration advice.