I can only give basic advice without knowing the model of your toaster or what you mean by "following all suggestions"..
Let's make the assumption that you have cleaned the mechanism thoroughly as I'm sure you have.
You seem to realise that contacts can't be loose, so with that elimated, cleaning hard to reach contacts can be done with a spray-can elecrical contact cleaner ideally, but I often have success with a fine double sided emery board that the lady in my life uses for her finger nails. (hope she doesn't read this and realises why they go missing!!) Trim the emery board down with scissors to make it fit the job in hand.
The next thing to try is to lightly lubricate the carrier mechanism and see if that helps.
I'd avoid wasting any more time if these don't work and consider buying a replacement, cheap enough these days.