Is there not a fast track system, which of course they would charge you for. Whereby you can go in person and wait while they deal with you. Yes I know you went there before and had to wait, but it's Hobson's choice sometimes. I would advise you avoid the summer months as June July and August, are the busieast.
You can also consider 'Registerd Post' or Recorded Delivery' as options for sending your papers. That means it would be signed for on receipt.
You can insure a package, which would cover you for the cost of replacement, should your passport go astray again. Which on the face of it, is extremely unlikely.
I don't know anybody at the home office, just some woman at Inland Revenue ;)