Any insulation pros out there

I want to insulate my 2 1/2 car garage attic,the only thing is the ceiling drywall is nailed to 2x4's.I want to put a r-38 up there.I know it will be above the 2x4's but I won't be putting any thing up there to compact the insulation.Would that be ok,if not any suggestions.I do live in the south so winters are very mild.

why nit put in r11 paperback toward the interior and then overlay with r19 unbacked laid perpendicular to the joists/trusses?

If you have a completed ceiling already that has an access blow the Owens Corning product in it.

The above mentioned R-11 with R-19 on top works but is a major PITA to install...

When your done you've done twice the labor and still only have an R-30...

Using the blown in you can install as much or as little as you want without all of the crawling around on top of the truss's...

https://www.lowes.com/pd/Owens-Corning-AttiCat-R-19-Blown-In-Insulation-Sound-Barrier/50370322

We use R40 in attics around here.

I'd think in the south with the mentioned mild winters R 30 would be fine. Also believe that with the humid summers it'd be nice to have a more compact blanket. Surely shy away from cellulose products. I've had both in my homes and actually talked with an insulation contractor (40+ yrs exp). He prefers batts. He claims over time the blown in stuff compacts and only more can be added. Once crushed down the insulating factor goes down and difficult to add vapor barrier on bottom unless new const.
fwiw, use roll r11, and use the stud cavity (cut segments) for the transverse lays to cut down installation time.
Lastly I priced out buying insulation and for just a little more than my price he provides and installs. Benefit of buying truckloads of the stuff.

The higher R value is also better for keeping heat out during the summer. Insulation is one area you don't want to skimp out on. Also, don't buy
from the big box stores as the price is way higher.

Yes, that would be absolutely OK. The R-38 will insulate the space below the sheetrock ceiling. You won't be compacting your insulation, which is important to retain the R-38 rating. How is the air above the insulation ventilated? Are there soffit and eave or ridge vents? If not, you might want to put some ventilation (fans or vents) to circulate the air and reduce moisture in the air above the insulation.
Cheers,
- Art

Thanks for all the advice.I'm still deciding which way to go now.