If his problem is the water table then cutting into the slab is only
going to make it worse. *There is no certainty with anything but I'd
start simple and watch it for a while.........

cutting into slab adding french drain and wall drains with sump pump
will definetely fix the moisture problem forever....far cheaper than
the other way............

exterior drains sound great but are costly. execavate all the way
around your home, losing all plantings landscaping sidewalks patios
etc AC compressor may be in way cut down a tree or two to get bachoe
in back yard. have to dig BELOW footer level and even then a high
water table directly under your home you can still get water in your
basement. any paved areas must only be backfilled with gravel to
pavement level or pavement may tip or move, and even if you do it
perfect it may move anyway

scrub exterior walls super clean and paint with water proofingn and
add drainage membrame/

dig a ditch to daylight somewhere, hopefully your home isnt the low
spot of the neighborhood.

now regrade lawn the backhoe has things torn up and rutted, might as
well replace the gas line the backhoe bumped while digging, new
downspout underground drain lines too. now plant and water
grass.........

home finally looks nice, county asseor noticed and raised homes
value...and you needed building permit. nosey inspectors came
visiting, is so and so up to code?