That mortar idea is probably a bad one.
Look at another pan that is identical to yours, there are usually fins and pegs. The pegs sit on the ground and the fins are for structural support. The fins will block the mortar from flowing, not to mention...probably most of it will NOT make it to the back of the pan or even mid way.
IF IT does make it mid way, it will most likely fall into the hole that the drain comes out of. You don't want 20 pounds of mortar to fall on your head along with a half sheet of drywall in the room below do you?
Just a suggestion, but I would rip the whole damn thing up and start over, or just forget about it.
my tub cracked and creeked for 2 weeks and still occasionally does when we first got it installed. I was sure I leveled the floor perfectly prior and at first was pretty upset about it, then it subsided.
If you floor wasn't cleaned prior to the pan being placed down, it could also be hovering in some areas (not support) on dirt and debris and might eventually give.
Creating an access point is going to be pretty pointless unless you are working on the area that you turn the water on and off, if you are just doing this to get to the pan you are going to be probably surprised to realize that you will be staring at the side of the pan and MAYBE a 1/2" area where you might be able to look at the bottom.
With the footer plate of the 2x4 wall, you wont be able to put your head low enough to make a visual inspection very well.
You have a mess on your hands, and need to research much more prior to doing anything. I like what the other person mentioned about the foam, but the sand and mortar ideas are pretty poor ideas after the fact.
I would love to see pictures or be there in person to see what's up. Because I think I understand your situation almost completely but this is one of those things where you would have to see it to suggest a resolution.
If I were you, I would stop the leaks and live with the cracking sounds. If the pan actually cracks then yes you will have to do something about it but to do it right you would have to rip the entire project apart anyway.
I don't know many plumbers that wouldn't stand by their work either. Why aren't you contacting them or , if they are neglecting you - taking them to small claims court? They have 'or should have!' insurance so, you should be able to get your money. It sounds like this is a handyman and not a plumber. Big difference there. Were they insured?
I would never let anyone in my house that isn't insured do any work. Including friends, family, the pope, or GOD himself!