I think you need to sit on a "Ross" root feeder.

If you are of a mind to fertilize your trees ,plain old 10-10-10 or
5-10-5 broadcast lightly in the drip zone is mostly what you need to
do, a soil test would be great but a coffee can of fertilizer
broadcast over a few hundred square feet of drip zone is plenty and
cheaper than the test. Adding organic material is even better, a half
inch of sifted compost now and again won't even interfere with lawn
mowing. Or mow your lawn to discharge towards the tree and direct the
cuttings towards the dripline, trhe same goes for fall leaves.

Here in the Northeast I wouldn't fertilize much after the 4th of July
because you don't need to go into the heat of summer and into fall
with soft new growth, add the organic material and improve the soil.