Joe Eigo

I do experiment this year too, at least with some trees, which also got fresh mulch this year. I got a grass mower with basket for free and tried it out.
I d rather prefer to put the clippings on the chipped mulch compost to get it fired up for some reasons, but when the basket is full next to an olive, I felt happy to dump it there.
Be aware though, that long grass cuttings attract mice to live nearby.. They can cause terminal root damage to young trees.
The clippings also rot very fast. Within 3 weeks it's gone /over grown.so it's kind of a question if it's worth the time.

I like your approach. For the trees I would leave plenty of the small shots at the trunk and branch base to keep the juice running and avoid new dead wood, by accidental cuts.
Everything else about pruning and tree integrity comes with time. Better start slow and not do mistake. Don't bring a chainsaw, a simple pruning saw is enough 😉
For your hard ground you could introduce pioneer plants like mustard or line. They are both a pain in the ass to cut though, but they do the job well to crack the soil.

You don't want to have big bushes under your trees as it makes harvest a struggle.
I would recommend leguminoses for nov-april and portulac as a summer coverage. Leguminoses work well with olive chip mulch (also fresh) and gets cut before summer. Portulac can handle the harshest hot conditions, grows very shallow and catches morning dew in the summer. It keeps the soil cooler and dies off in autumn.

Plowing is the worst thing you can do. Erosion is one thing, second the trees rely on their fine root system near the surface to catch the morning dew.  What happens when you rip them?
I think they just do it because it always have been done that way as every generation had to work with a dense powered soil after winter rain. It's the reason itself why it's done.
I haven't plowed for 4 years and the results are incredible!

4 years into mulching all cutoffs I can confirm there are a incredible amount of mushrooms finding a habitat in the mulch. But just good ones. If you have deceased branches you better burn it or it will transmit to other trees by mulching. I will definitely going on with that practice until I get too old, as I see tremendous value for soil buildup and health, wildlife and tree health.

I wouldn't recommend to use any leaves from the mills, as they contain everything farmers spray in high concentration. That's a mulch for the I don't care quality farmer, not for the I eat my own product farmer.

I m doing the chipping of olive branches now for 4 years and got some experiences to share.
I chip branches where I remove all wood >2cm with a machete with a old Scheppach Biostar 3000 3phase machine. Off-grid 😎 It's a wonderful cheap machine and far more quieter then gasoline driven. In addition kickbacks which happens sometimes when inexperienced kicks the stuff by design upwards and not in a 45°  angle in your face. Definitely a recommendation for safety. Btw. Never wear gloves when chipping, thats probably the biggest danger of using the machines.
I chip the branches of healthy olive trees beginning with harvest within 2 days. Deceased branches would need to get burned, or the mushrooms spread. Until January it's possible to apply it directly to the olive trees. This way you avoid the nitrogen sink to affect the flowering stage. Seeding leguminoses in December January on top of fresh clippings around the olive trees works far better then expected. They have no issues to germinate and should balance the nitrogen sink even more.
After January the chips get used as bedding in the chicken coop or are composted on a big pile together with grass clippings, and some biochar. The compost takes approximately 4years to be good enough for any veggies. After 3 years  the soil looks great but cabbages for example don't thrive yet in it.
In spring is a good time to clean out the half composted chips and spread it under the olive trees. This manure mulch is a really effective fertiliser.
Chipping is a great Ressource, builds up soil far quicker then expected and is free. I don't buy any fertilizer or chemical sprays, don't till and the trees shows no lack of nutrients at all!
It also keeps the soil moist for an additional 1.5 months in summer without the need of watering.
As a beautiful side effect in autumn you gonna walk through a mushroom paradise.
It just need some extra effort 😉