Beech is fairly shallow rooted, so removing the bulk of the root ball should be fine. You need at least 4"/100mm of concrete, if your van is frequently heavily loaded I might be tempted to go to 6"/150mm, possibly with reinforcing mesh at half depth. Fill to the bottom of the root ball holes with concrete or backfill with rammed MOT Type 1. Don't backfill with soil or a void will develop and the concrete could crack.
I would just prune back the lower branches regularly.
Cheers, my van will continue to be parked where it is in that photo as I can back it tight up to the garage doors and hedge to prevent scrotes trying to break in. I'm widening the drive so that my wife's car will fit in when I'm parked up so 4" of cover will be more than enough.
Beech is fairly shallow rooted, so removing the bulk of the root ball should be fine. You need at least 4"/100mm of concrete, if your van is frequently heavily loaded I might be tempted to go to 6"/150mm, possibly with reinforcing mesh at half depth. Fill to the bottom of the root ball holes with concrete or backfill with rammed MOT Type 1. Don't backfill with soil or a void will develop and the concrete could crack.
I would just prune back the lower branches regularly.