I'm assuming when you say "raised bed" it's still sitting directly on top of the ground?
Palms are very shallow rooted. 3 m is close enough for it to invade your veggie garden and suck up a lot of nutrient by way of fine roots.
I agree the shade probably isn't the problem, but the outer palm roots may have formed almost a "carpet" underneath your garden bed, that's interfering with proper drainage and may cause your soil to go a bit sour.
Weed-mat probably won't help much, but it might help a bit. You can buy a little bit at hardware shops for a small cost.
I would trench along the outside of your raised bed between it and the palm. Dig down and sever off any roots you find, with a spade. Go as far down as you can manage without wrecking the garden - but deeper than the bottom of the veggie bed. Then insert a barrier between the veggie bed and the palm - anything you can find scrap-wise like offcuts of that plastic stuff you put on pergola roots (grasping for a name??)
I would also consider raising the veggie bed again, if that is possible, to get it clear of any potential clogging underneath. Well-weathered bricks would probably be OK, then start off again as you would with whatever you intend to add to get it going again.
Good luck anyway, just my thoughts

you could put in a root barrier might be expensive but!

we had raised beds where the roots of radiata pines invaded, our gardens did well enough(the wrong aspect didn't help much).

maybe you need to look at your medium and how you feed it, we had our composting worms in the garden and tucked scraps under the mulch daily. will post a link to those very gardens.

also do you mulch? we lay mulch up to 8"s deep spoilt hay or sugarcane.

as alison says maybe time to raise the beds even more we are getting older so now we use corrugated for raised garden edges.

also on our site we have a feature on using bales for gardens.

keep in touch

len

Here is a link that might be useful: lens building a garden

that looks terrific, Len, no bending once the hard work's done.

that's it alison,

do the hard work first, but boy saves the back, planting harvesting very much a breeze.

how are you i don't think we have chatted for ages? these forums sort of snailed right out.

len

I had the same problem with gum roots.Now I put a 50mm concrete base under all my beds .No problems

Here is a link that might be useful: growing organic vegies