Hi Michael,
The problem is we are having difficulty getting the products within p= indexed*
If you have a canonical set on a p=* to the base URL, this will mean those pages never get indexed by Google.
If each page is different /p=1, /p=2 et al, then a rel prev / next will handle this for you. However, it depends on what is on each of those pages. If they are virtually identical (or at least very similar) then the solution might be to leave the canonical in place - but that doesn't sound like what you want.
If what I am reading is right, the nel=next & prev would work for you - but remove the canonical on each page. You could also use a view-all as this will work, but have a read of some of the options here. It covers what you need to know.
https://support.google.com/webmasters/answer/1663744?hl=en
-Andy