Organic... dig out as much as possible
Mechanical... stump grinder
Chemical... apply chemical to stump to end growth potential.

FWIW i dug up a stand of banana trees in when i lived in hawaii to make room for garden and cut down on mosquitoes ... turns out they are as hard to remove as your hardwoods appear to be ;-)

They came back with a vengance

Hire someone who knows how to dig to do it for you.

If you were not in a hurry you could smother it.

just pee on it a number of times....it will burn the plant

This is when backhoes come in handy...

"just pee on it a number of times"

Pee makes an excellent natural fertilizer for trees.

Heh, palms are surely not "hardwoods". Technically, they're not even really trees!

+oM

I've never seen, nor can I easily imagine, a good definition of the word tree that would exclude palms while including all other "trees".

Here is a link that might be useful: List of Tree Genera

dricha - Today my husband took an axe and hacked through the stumps. He'll work on it throughout the week, then try to dig it out this weekend.

I'd still like to know how we can kill the roots without toxic chemicals. I've read suggestions on another forum that one way is to take a drill, going down at an angle, then pouring salt in the holes. Has anyone tried this?

formandfoliage - Maybe a toy backhoe could fit in this tight corner. ;)

Pouring salt in stumps may be more harmful than the measured amount of herbicide required to keep a stump from resprouting.

The assisted decay method isnt normally salt or rock salt but high nitrogen fertilizer .... often not very organic.

The organic answer is dig 'em up ;-)

Here is a link that might be useful: another way...... of many

I use a sharp shooter and as above, a mattock. I'm assuming you want to plant where your digging out the roots? Salt would be worse than using a chemical. Have a picture of the area?

I don't know about your husband but mine digs a mean hole when he is super annoyed about something.
I usually pull up a chair and a lemonade while he is working and spout off carefully calculated snippets designed to push his buttons.

It's not malicious- we are twisted :) and it is our decades long method of digging out stubborn stumps.

cearbhaill - When my husband is doing hard physical labor, he's really, really quiet. I just do the same thing as you did, and he stayed in surprisingly good spirits. ;)

formandfoliage - You are too funny. Only a toy backhoe would work!

The latest - Now, he's thinking of burning it. That's making me a little bit nervous.

could anyone suggest various makes of toy backhoes suitable for stump removal?

Stumps from Beetlejuice?