Shopping around for funerals by telephone is basically a waste of your time and energy.
Go to the funeral home, get their quote in writing, and the length of time that this quote is valid.
Take that quote to the next place you go, if their's is higher, ask what the difference with between this $5000 quote and their $6000. Then when they give you a $4500 quote for something similar, take that to another or back to the first one and ask them if they can beat the price if you are willing to leave a deposit now.
Most people making funeral arrangements are doing it under pressure. If you can do it ahead, you can save thousands.
I've helped make more funeral arrangements than I care to remember.
PS, also remember there are casket brokers in the US now, you don't have to pay full price at a mortuary. You can buy your own and have it delivered. I haven't done that, but hear you can save a lot.
Edit: As for the one that said you'd "piss off" the funeral director, HA!!, I'd like for him to show that type of attitude in front of the OWNER. He'd be fired. The mortuary business is hurting BAD in the USA. People are going for direct cremations, cutting costs, and only a few doing the high end caskets. It is a competitive market.
Oh, and never pay for that "special seal gasket" which is supposed to last 50 years....my line after that is, "and then what??" That shuts them up. Unless you are trying to preserve a body forever, most of us expect it to decompose eventually, so what is 50 years in the course of the world?